To keep your account secure, you should never share your account with anyone. You should never give your password to anyone.
The only information that is safe to give to another player is your Character Name.
You should make sure to use a password that is a minimum of eight characters long, that is alpha numeric, and case sensitive.
You should not use the 'save' functions on your username and password on a public computer. Use those only on your private computer.
It is best to not play on public computers. However, if you play on a public computer, please make sure to log out of the game completely when you are done. Close all the browsers on the computer that you were using, as well. This will prevent others from logging into your account.