There are literally thousands of websites and books with tips on internet privacy. Ultimately, all of their advice can be summed up in one simple rule: behave on the internet exactly as you would in the real world.
Firstly, this means not giving out your personal details such as your phone number or address openly. Writing your address in a private email to someone you know in real life and can trust is fine, but writing it openly on a social network or on a public forum is like scrawling your name and and details on a billboard – it means that anyone, including criminals can access that information. You wouldn’t make that information public in real life, so don’t do it online (unless you actually do feel comfortable writing your address on billboards in real life, in which case, power to you).
This applies to other kind of information too – whether it’s a personal story that you wouldn’t want people to find, or a compromising picture of questionable shenanigans that you wouldn’t want an employer to see. If you wouldn’t place on it on a public noticeboard in real life, don’t do it online.
The information that tends to be most damaging when released is personal financial information. Most banks specifically state in their safety packs that they will never ask you to verify your details via email. If you’re ever unsure about the authenticity or safety of any online transaction or other kind of communication regarding your bank account, don’t hesitate to contact your bank and ask them for advice.
Finally, please ignore any emails you receive from a “Nigerian prince”. Nigeria is a democratic republic.