Do you have access to MySQL or similar? I'm sure there are modules out there that do this sort of stuff, but if you want to make your own, what you would do is setup a users table to store unique usernames and passwords, and a sessions table to store info about current sessions. You populate the users table however you want - online signup, whatever.

When a user logs in you give them a cookie and record the session in the sessions table. Every time they request a page you check the sessions table. If it is > x minutes since that user last did something you log them out (reset their cookie) and ask them to log in again. Otherwise you update the timestamp on the cookie.

Guy