As you don't have the disc available, and don't know the password already, you're in a bit of a pickle.
Follow the step by step process of this website, and you will be able to reset the password. Be very cautious and type ONLY what you are told via the steps, as you're using the equvilent of Terminal, you could without too much effort muck up your Mac.
As i said though, I've done this a thousand times, if you follow it word for word, character for character, you'll get your password reset.
Good luck mate,
There actually is a slightly easier way in OS X 10.5 or greater.
1. Start up in single-user mode (hold Command-S as the computer starts up).
2. Type: mount -uw /
3. Press Return.
4. Type this:
passwd (user's short name)
Replace "(user's short name)" with the short name of the user account whose password you wish to reset. If you are not sure what the account name is, you can get a list of user names by typing: ls /Users
5. Press Return.
6. Enter a new user password.
7. Press Return.
8. Type: reboot
9. Press Return.