The technique involved is a program automatically trying multiple login attempts quickly (called: brute force). You just let it keep running until it has used all of the attempts it was made to do, or got a successful login. Either you can write a program to do this, or search for one already made.
You can also manually attempt common setups. Like "USER admin; PASS admin" or "USER administrator; PASS password" or whatever you can think up.
Keep in mind that ftp servers usually keep logs. Another defense they may use is automatically banning you after so many unsuccessful logins. For this reason, the technique I told you about above is not very effective, and you shouldn't waste your time trying.
You can also try figuring out what kind of ftp server software they are using and search for exploits for that particular software. This way it won't matter what password or user exists, you can get access IF it has a bad enough exploit.
I hope at this point you will go do your own searching.
