Noob: How to refresh ROM on Nexus S?

Hi All!

Really hope you'll help me out. I'm recently off Symbian S60 and there it's not really a question on how to refresh and install ROM.
I'm totally new to Androids and I'm not sure what to use to refresh my ROM. I use the phone for a month now and I see that sometimes it does not work right:
1. Tried to add a contact and it showed that it saved it, but it did not appear in the list
2. Android Market always crashes when I click "Recently Added"

So, I decided to tey Cyanogenmod or newer Android versions, but I don't really know how to install a new one and back up my data.

Will appreciate your help!
Thanks much!!

P.S. The phone is not black and official unlocked Nexus S, so it's not the problem with the phone.