You can't. There are places you can go with your notebook which won't have any access at all (well, except for the mucho expensive satellite phones, and then only at a very slow speed, if at all).
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ISPs - your route to the Interent
You must be connnected somehow (regardless of all the marketing gee whiz terminology) to a computer which is already connected to the Internet. This computer is generally onwed by your ISP (eg, AOL, Earthlink, NetZero, PeoplePC, the cable company or some such). That connection to an ISP is generally over a:
1) dialup telephone line (or mostly equivalent in an abstract sense, cellular or satellite phone) to a modem bank at an ISP computer or computers (serial or USB cable + phone line),
2) through a DSL connection over standard telephone wiring (limited distance from your local "central office" building) (wired phone line to DSL 'modem' to Ethernet), or
3) through a cable TV cable and the local cable company's ISP arrangement (cable to "cable modem box" to Ethernet).
4) in future, via telco optical fiber (if available and not generally now, nor probably for quite some time in the future for non-commercial use). This would be super DSL, be faster than lightning and may happen. Real Soon Now.
In every case above, a wire or line is required to connect your computer to something which (eventually) connects to the Internet. And each of these cases has vey definite length limitations (10 feet, 50 feet, 100 meters, ...). If you want to run your computer somewhere beyond that reach, you will have to do something else.
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wireless
So use some kind of radiation instead, right? Infrared is a possibility, but its range is very short (within a small room) and somewhat slow as the IrDA standard hasn't been upgraded in some time. Wireless USB (not yet available) and Bluetooth are both short range (though the new Bluetooth spec is more generous, though not actually available in real equipment yet). Mesh networking (ie, ubiquitous, autonomous, self-repairing, micro power relay systems) is entirely possible, and might be made to work sufficiently fast, but there are many problems (mostly who controls and bills for it, not technical ones) before it's even close to availability. Mesh WiFi systems have already been prototyped and will probably be available as private, enthusiast-supported, utilities in some places well before Zygbee or any of the other proposals are ready for even limited deployment. Indeed, several cities have decided to offer WiFi (not mesh WiFi, but the tradional sort) to their citizens as such a utility. Indeed, New Orleans, having been largely abandoned by the exiting telco, cable, and wireless operators in the immediate aftermath of Katrina, has forged ahead and may be providing a demonstration model for others.
That essentially leaves you with standard WiFi, the assorted 802.11 schemes, unless you live in one of those pioneering places. Of the standards, b, g, and n have better range (at 2.4GHz) than a (at 5GHz), and the original 802.11 (at 900 MHz) had better range still but was a good bit slower than a, b, g, or n. There were considerable interoperability problems with 900MHz gear, so unless you can find radio equipment all from one vendor, avoid it. Support, both hardware and software will be patchy at best as well. Range for the b/g/n variants is several hundred feet at best (at reasonable speeds), with the usual rubber ducky antennas, and less for the builtin antennas in most PCMCIA (or PC-card) WiFi cards.
For the moment, unless you want try out one of the new cellular phone 'modems' (currently very expensive and incompatible from one carrier to another), which will have the widest coverage area of the non-satellite systems, this is the best you can do.
Working range depends on the power in the WiFi adapter, match between the antennas at your computer and the one at the access point (which is of course attached to the Internet via an ISP of some kind), and on the speed desired -- higher speeds require higher signal power at the receiver, all other things being equal. The match must be such that the signal strengh at both ends is sufficient to support a data rate / modulation scheme fast enough to be actually practical. There are several factors which affect adequate signal strength.
1) The radios themselves can be more sensitive (measured in -dBm and the lower the number the better. It's only rarely mentioned in sales literature). Some specification sheets give this value, others don't. All should since the radios vary considerably on this issue.
2) The radios can be more powerful (but this has a definite upper limit in law and regulation in the US and -- slightly differently -- most everywhere else). Actual WiFi radio equipment varies a good bit in the power possible, from 10 or 15 milliwatts at the low end to the practical legal maximum for this kind of operation, 200mw at the high end. There are other implications here, however. A laptop battery will get drained a good bit faster if using a high powered radio, and higher powered signals can be snooped on from more than merely across the street, raising an increased security concern.
3) More directional antennas are possible, if often tricky. Some radio equipment doesn't make provision for an external antenna and in practice these make improvements at this level impossible. These radios should be avoided. However, thses antennas are harder to use in many cases as they must be correctly aligned with each other, and be quite stable physically. Very highly directional antennas (often 'dish' types) can be disturbed, taking down the link as a result, or even destroyed, by quite modest winds. Secure and solid mechanical mounting is an important issue. Unless you're sure where the other antenna(s) is/are, you will need one or more of great patience, special software (which works with only some radio equipment), even more expensive RF test equipment, or cooperation by the access point operator (not usually available), to set it all up. Properly done, very directional antennas can greatly increase effective range (to several miles instead of fractions of a mile).
4) Since interferring signals are merely noise -- from your perspective anyway, reducing the level of those signals will help. This is harder to control since b/g/n WiFi operates in an unlicensed frequency range (the Industrial / Scientific / Medical band around 2.4GHz) shared by several other services including some cordless phones, some garage door openers, leaky microwave ovens, some 'baby monitors' and wireless Web cameras, other WiFi operators, etc. These are hard to locate in principle, though in practice may usually be neglected if the two WiFi radios are 'close enough' together that their signals swamp the 'noise' from the existing other sources. This dodge reduces working range and is not usually accepted by users without hostile sotto voce muttering. And of course, the interferrence situation will change rapidly and unpredictably as equipment comes to life and shuts down. The same type of interference problem arises with 802.11a WiFi operation, but, at 5GHz, those signals have substantially less range as they are more easily blocked by such things as walls and tree leaves, and so a isn't as useful for covering large areas.
5) Make sure the signal polarization emitted/received by the antennas at each end of the link match. Mismatches can easily make an otherwise workable link completely unusable. This is a quite separate issue than antenna directivity, which applies equally to all kinds of polarization. Note that most consumer grade WiFi routers and access points (certainly those with the vertical 'rubber ducky' antennas) emit (and receive) vertically polarized signals, while the card adapters are typically horizontally polarized when the laptop is flat on a work surface. Card adapters with a rubber ducky antenna can, of course, usually be adjusted. Polarization for laptops with inbuilt WiFi equipment can't easily be predicted as the internal antennas can be installed either way.
So if it all works well, WiFi availability will be patchy, depending on how close you are to the nearest available access point, on how crowded that access point is, and on how much the operator wants to charge for the service. The limited number of available b/g/n channels, and the inherent overlap between them, prevents more than perhaps 4 (of 11 allowed in the US, more in most of Europe except Spain) being in operation simultaneously. Again, a offers an improvement with more (and less mutually interfering) channels, but its reduced range probably cancels that out for the sort of application you seem to be contemplating.
If cost is no object, I suggest you play close attention to the (multitude) of somewhat high speed data offerings from the cellular carriers. Laptop PCMCIA cards have been available for some time for several of these. The field is quickly changing (and differently in various jurisdictions) for technical, marketing, and regulatory reasons, while any agreement with the carriers is typically for at least a year. Use some caution, actually read the fine print, and look for a contract offering unlimited data transfers, or priced so as to depend on the amount of data transferred, not merely a high flat rate whether heavily used or not.
Another future development is WiFi Max (yet another 802.11 standard). This promises both higher speed than a/b/g at perhaps 70Mbps, but also greater range (several miles). It is specified to operate over relatively long distances (miles), but will probably not be a consumer item for quite a while. It has been designec to operate over a very wide range of frequencies, from 2.4GHz to about 50GHz. it will probably be used as a long haul connection between networks, and not a node to node link.
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security
Since radio signals of any kind are 'in the air', they can be eavesdropped by anyone for any reason. And generally without leaving any trace of the snooping, so you won't be able to tell. They can also be hijacked in the sense that the radio signal itself can't be distinguished from any other radio signal, and radios will usually latch onto the highest strength signal, which might have been you two minutes ago, but is now soemone else who may be able to pick your Internet connection in midstream. This is a physical embodiment in many ways of the abstract 'man in the middle' attack from the crypto literature.
Security on broadcast radio links can be handled in several ways. WiFi access points can refuse to attach to signals coming from radios not on their 'approved list'. Or they can decline to broadcast their presence (via 'beacon packets'), inviting attachement, and instead require the remote user to explicitly request one. This last is a sort of 'security through obscurity' measure, and should never be seriously relied upon. Used on the general principle of making life difficult for attackers, if only a little in this case, but never relied upon. Remote users can be required to go through an authentication sequence before being permitted use of the access point (802.1x is a standard which includes such arrangements), pushing off the secuirty issue to a higher level in the 'protocol stack'. And signals can be encrypted so even if overheard, they will be useless meaningless gibberish. Unfortunately, the encryption in WEP, the first WiFi security standard, was grossly defective. No actual cryptographers were consulted, demonstrating yet again that even technical experts (in something other than crypto) can be publicly led astray by crypto subtlities. WEP should be used, if it's all that's available for your equipment, but not counted upon for much.
The 802.11i security standard has been partially iplemented (as WAP) in some equipment, and more fully implemented (as WAP2) in even more recent equipment. Properly configuring it requires some actual understanding of both crypto and the operational context, so WAP is more difficult to use correctly than WEP. As always, poorly configured crypto systems can be fully (and silently) insecure, so care is absolutely required.
WEP, WAP, WAP2, and probably full 802.11i can be implemented in hardware included in the radio (and configured in software in various ways, eg, via a Web browser) or can be implemented in software running on the attached computer. The handshaking mechanisms in WiFi protocols are already time-consuming, but adding more in a security scheme will inevitably consume more tim, so the time from request to attachement with the other radio will be longer, and the crypto processing involved can be set up to require considerable computation. If so, the available CPU capacity (included in the radio hardware, or running on an attached computer) can be heavily used. Slow processors can bog down if so. The hit on effective throughput over the radio link from using security protocols can be substantial. Much of it can be avoided, even on old, slow, CPUs by judicious crypto and authentication choices, but this requires background and contextual knowledge most users won't have. Since, in general, you control only one of a radio link, there's not much you can do about a slowdown at the other end.