I disagree with the above poster.
VPN are secure but NOT anonymous. They create a secure "tunnel" from you to the site you are connecting to. The VPN services do know who you are and what what data you are transmitting and receiving. Many VPN services will keep logs and WILL turn over those logs to law enforcement. How do you know which VPN services will not? There is no way to know. So it is best to not use them when your aim is to be anonymous rather than secure.
Tor encrypts data from your machine, through your ISP (they do not know where the data is headed nor the content) through several nodes in the Tor relay. Each nod removes a "layer" of encryption just to know where the next relay is. Each node does not know the content, where the data originated, nor the final destination. Once it leaves the last node then the data is completely unencrypted and sent to the site you want. Since it is unencrypted and not under a private network anyone can see this data, BUT it does not matter because there is no way to know who sent/received the data.
https://www.torproject.org/about/overview
Here is a picture representation:
https://www.torproject.org/images/htw2.png
I highly recommend to NOT USE The Tor Bundle. This is because governments have and do target Tor users.
http://jolt.law.harvard.edu/digest/internet/snowden-documents-reveal-nsa-attempts-to-track-tor-users
They have and will find flaws in Windows and Firefox to spy on people.
https://blog.torproject.org/blog/tor-security-advisory-old-tor-browser-bundles-vulnerable
This flaw has been corrected, but they exploited it for years before it was discovered. They may be exploiting another that we do not know of.
Does this mean that Tor is vulnerable? No. Tor has not been compromised, just some of the software to use Tor. Many will also say that the government controls many Tor nodes. This does not matter because they would have to control ALL nodes. Since each node does not know where the data came from nor where it is going then controlling many nodes does no good.
So what software should you use?
DO NOT USE WINDOWS. Nor use your every day OS.
Put either Liberte Linux or TAILS on a USB and boot into it.
http://dee.su/liberte
https://tails.boum.org/
The Hidden Wiki (AKA deep web) is over rated. Not as exciting as you would think. Also if you are easily offended, stay away.
Since Tor routs you through many nodes, it is slow. The point is to be anonymous, not fast, secure, or anything else.