I recently went through the process of registering my residence.
In my case (Gangxia area) it was pretty simple.
WARNING: This was the procedure in my area. Yours may differ. Taking along a Chinese-speaking friend is advised. You may also want to be prepared to return home for something not on this list.
1. Ask your building management which police station to go to. It shouldn't be too far beyond walking distance, since it's the station for your area.
2. When you arrive, look for a separate door, or at least a window in the main office, that says something like "Residence Registration." It should be prominent, as ALL residents, Chinese included, have to register their domiciles.
3. Take along:
--a photocopy of your passport's ID page and visa page
--2 2"x2" passport photos
--an "original copy" (not a photocopy--probably a pink carbon copy) of your lease
4. There's a form to fill in. Mine was bilingual (Chinese/English) and I could have done it myself. (But I had a Chinese speaker helping me.)
5. They will give you a typed version of the form you filled in. Check it carefully. Mine had a few typos.
6. When it's finished, you get one copy of the stamped form, with your picture attached. They keep the other. Keep this in a safe place for the day when they knock on your apartment door and ask for it.
There was no fee. I didn't have my lease with me, so I had to return home to get it. If I hadn't, the whole thing would have taken less than 30 minutes (only one person in front of me in line). Look for a number system, and take a number as soon as you enter, even before filling in the form.
It was that easy. One caveat: Whatever visa you show, its expiration date will be the term of your registration. Ironically, I was trying to beat the July 1st deadline, but my visa expires June 30. So I'll have to do this again when I get back with my new visa.
Also, I'm not sure, but I suspect this will only work with a Z visa. Business and Tourist visa holders should be staying in hotels or with relatives, NOT holding leases. if anyone knows otherwise, please post a reply!