I'm assuming it's second hand or you're not the only user; whoever had it before you set Firefox as a login item, so it opens automatically.
To turn this off, go to System Preferences, click the Accounts item, and on the "my account" item click the "Login Items" tab. You should see a list that includes Firefox; select it and remove it (minus button), and you're good.
However, if this is a used machine, you really should at least create a fresh user account for yourself if not completely wipe the computer and reinstall the original software from the discs that come with it.
If you just want to create a new user account, in that same Accounts preference pane, click the lock icon and enter an administrator password, then click the plus symbol; this will create a new account that you can select a user name and password for, and won't have anything pre-set. To boot right into that account, select it under the Login Options item.
If you don't have the admin password for the computer (and you're the only user) you're going to need it eventually, so a clean install is probably in order.