Staying safe on the internet really depends to what you do,the most threats of the internet are only affecting computer's health and the user itself.
Here's my few cents:
About computer safety,there's a lot of protection software in the market which works like a charm.
The worst case of an internet threat for computer's health is getting your personal information leaked to third party like credit card info,billing account,etc,even leak your home address and getting stalked by strangers.
Well for that many software will help but user should double check out if the place you send the info is safe.
Personally i'd recommend having a Hardware Firewall (NOT Software,though a Software Firewall would be appreciated),and a Security Suite of the user's personal choice,it should be having a Combination of Antivirus/Antispyware suite and a feature to check Webpages for possible threats.
For Unix Operating Systems i'd also recommend to have a Firewall System and Antivirus Suite.
It is required for the user to have an eye to NOT accept any invitation or file by for example a messenger's contact,or click on a link,visit a website,install a program without doing this on purpose,because a virus can insert a computer even by staying in Operating System's Cache.
That should keep safe any computer.
Personal Passwords:
Your passwords should be as big and difficult is possible,if you can't remember them write them somewhere safe.
Use mixed Spanish,Japanese and Greek letters,capital and not,Hexadecimal,and ASCII characters when it's possible,otherwise use allowed symbols mixed with numbers and letters.
For example the password "!!@@$%%^&*()" is big but EASY to guess,the password "@*8^2¿~♦jO⌐λ" is smaller but HARDER to guess or even break,and don't use the example.
Online shopping:
Use a different username and/or email than the one you use on Web Forums or Social Networks and always buy with Cash or Delivery or with trustful services such Paypal.
Beware several scammers out there who wants your money,no you will not receive goods for half their price by a wholeseller,and no you will not win anything if you buy something else.
Failure to keep your online shopping info secret or using info that leads back to you by for example a username can be very dangerous and can help people to get to you.
Now the complicated part: Personal safety.
As i said before physical damage by internet or an internet user is in rare state,however psychological damage is not.
It's hard to keep everyone away from having a user profile on famous Social Networks,if you do it you should stay safe.
Here i'd recommend these steps:
For protecting yourself physically:
Adjust your privacy settings to the highest.
Select to NOT accept any messages or friend requests by strangers and don't answer to them if you are sure you don't know them,and also hide yourself from public search and the Network's search feature.
Yeah if a friend wants you on a Social Network and wanna search you by email,he or she should send an email to ask you if you have a profile there.
If it's possible don't use your real name and last name on the public profile name and use it on a private profile description if you really want to.
Don't use a photo of yours as a profile picture which would be available to the public,use one of your favorite super hero or movie star instead.
PICTURE Safety:
Try to not upload any pictures on the web which shows information which can lead anyone to you,such car plates or road signs.
Also important is to NOT upload or send anywhere any picture of showing your house's garden,backyard,or even door.
The ugly truth is that by knowing the area i should search in,i was able to spot a house only by a useless detail such as window's color or garden's flowers MORE THAN ONCE.
Keep personal any photo of showing expensive cars,expensive things,money,collectible or and priceless items.
Do the same to Videos,and always double check if any of the above rules are applied before publish something.
What to say and what to not to keep your psychological harmony:
Keep your conversations with strangers low and don't mention any personal info even if you're talking online to a friend,and if you disagree with anyone do not take the thing away further,you don't know to who you're talking about as he also not.
There are some cyber bullies out there that wanting to see you go off and getting psychological harmed by trying to attack you or make you feel bad about your opinion.
Just stop the conversation and don't answer like you got harmed even if you did,such persons leaded a lot of "weak" feeling people to suicide or mental problems,it doesn't worth it,most of them are people with no life other than a keyboard and a screen.
That's all everyone,i hope my few cents will help all of you to keep yourselves safe on the internet.