Adjustment of status is same as applying for green card. You will do it with form I-485 and you also need:
Fingerprint laws has changed few times lately. For example I was fingerprinted first time when INS didn't have special requirements for fingerprints.
My fingerprints were bounced back as laws changed in April 1997 and they required that fingerprints must be taken by designated fingerprint service. I received this request after I got my green card . Well, I did it properly this time and went to Hayward police station as they were DFS.
After submitting my fingerprints again I received mail from INS again. They asked: "please advise us the reason why submitting fingerprints." I went to local INS office to ask what should I do and I was told not to worry as I already was granted a green card and INS shouldn't do that before getting fingerprints OK'ed in FBI. So I suppose everything is fine right now...
DFS system is defunct nowadays. Today you must go to "LEA" and take your fingerprints there. INS will give you list of LEAs on your area and FD-258 as request.
I have heard that this is sometimes very tricky. Some places don't issue EAD to you like I got it: they took my pictures and gave it to me same day I filed my I-485/I-765. Some places send it later.... so what to do after K-1 expires and before EAD arrives? Some people talk about "receipt rule", a rule that says that if you have filed I-765 and they haven't answered to you yet you could work under that rule. This is where you should be careful... I have heard of some cases where an alien had to stop working because K-1 expired and he/she didn't have an EAD yet. But I have heard this problem is under investigation right now... any comments about this?