Never, ever give out your real name, age or location. Even if it is someone you've talked to a lot, it doesn't mean that they're a friend. Use actual e-mail addresses, acquired in person, to discuss any personal business online with a friend. Do not air anything truly personal/confidential on sites such as facebook. If you wouldn't shout it from the streetcorner, then it shouldn't be on facebook.
If anyone you are chatting with in a game or on facebook that isn't a real-world aquaintance starts asking for personal information, especially age, leave immediately and do not respond back to them. People can also more subtly fish for your age- asking for your favorite bands and movies for example- that information can tell a lot about how old you are.
If a site tells you that you can only proceed if you click on this button or this ad, leave immediately. There are often viruses and malware associated with those. Never click on an ad and buy. If you weren't going in search of it, then you don't need to buy it. Those are often scams.
Only shop online through reputable dealers- amazon.com, e-bay, if you have thoroughly scrutinized the product, or the online version of known real-world stores. Doing otherwise risks your credit card.
Never open attachments that you weren't expecting, even if it comes from someone you know- viruses can send themselves through a friend's e-mail.
Never let others use your computer- you never know what they will do.
Disable most of the options of facebook or don't use it- especially disable the option to let others 'check you in' to a location. That is extremely unsafe, as it tells the world where to find you.
Don't post home photos online, especially from a phone camera. Those have GPS embedded in them, and with the right software, can be used to find you.
Don't post pictures of yourself.
Finally, if something or someone sounds too good to be true, chances are, it/they probably are.