Leave the fire control parts alone. Removing them for cleaning is a major problem with the M16/M4 family. Brush the dirt, blow it out, whatever. Routine removal will accelerate frame pin hole wear, etc.
You need to know how these parts come out, though, and if the weapon is truly filthy, choked with mud, etc. you'll need to disassemble it.
Start with separated receivers.
1. Push the hammer pin out. It's secured by a J-clip in the center. It will come out with the spring attached. Leave it attached.
2. Push out the trigger pin. The disconnector will leap out so catch it, then remove the trigger and disconnector.
Reassembly is the reverse (as they say).
Easier to put a short slave pin into the trigger to hold the disconnector and trigger as an assembly. Push the little pin out with one of the long pins when it's in the rifle. Hammer and trigger pin are identical. The hammer spring legs go over the trigger pin. One secures that pin.
TM9-1005-319-23P (Rifle, 5.56mm, M16A2) shows these parts. Some subtle differences you'll quickly figure out. The selector can stay in the 15-22 to do this. The TM is on line for download as a PDF.
-- Chuck