Not sure of current requirements but you need to bring a few things. Here what I had to provide from time to time:

Have at least 2 passport type photos (They might be using vidcams now)

Photocopies of your passport ID page and your visa page. You need to have your passport with you as they also check for your most recent entry.

Lease or contract for where you are living. Should include landlord's ID.

Residence registration is computerized, pretty fast and painless. Usually the ladies are helpful. Being a few days late usually is not a problem. If you don't register and they come for you it is a lot less pleasant.

I only ever bring photocopies of the passport photo page, visa and entry stamp.

I seem to recall way back on the first time that we had to bring a photo, but haven't done it since.
There may have been a copy of the lease the first time as well but my memory is fading and my wife would have handled all that.

My daughter has gone late more than once, but it wasn't first time registration.

Thank you everyone! Great info here.

The lease is mandatory now. Just a copy will do.