There are two differing schools of thought on two different aspects of peep shooting, but there common aspects are this:
1. Get a good solid cheek position. Keep this consistent. Consistency aids accuracy.
2. Roughly center the front sight post in the peep.
3. Now, look THROUGH the peep and concentrate on the FSP.
4. Place the FSP in the target. The target will be fuzzy. The rear peep sight will be very fuzzy, or you'll "lose" it completely. The FSP should be very sharp.
5. Control your breathing, and pause.
6. Squeeze the trigger gently, until it breaks.
7. Follow through (hold that position for a moment, then back off the trigger until it resets).
8. Lather, rinse, repeat.
The different schools of thought center around cheek position and placement of the FSP.
The .mil teaches 'nose to charging handle' to get your eye close to the rear sight and to use the charging handle as a landmark for keeping your position consistent. I know some very good shooters who like to back up more and use the 'wings' of the front sight assembly as a reference for how centered the front sight is in the peep. Both methods seem to work, but we're talking combat accuracy, not bench rest accuracy, and I have no idea if one is faster than the other.
The placement of the FSP is variously described as:
1. directly on the target
2. "pumpkin on a post" or 6 o'clock hold, or something just a smidgen more than that, where you can see a sliver of white between the top of the FSP and the bottom of the bullseye.
Criticism of holding the FSP directly on the target is that it can be hard to judge elevation exactly with a black FSP and a black target. Criticism of the 6 o'clock hold is that it is dependent on you shooting a black bull of such and such dimensions, since your point of aim is actually the very bottom of the bullseye, and your rounds impact a certain distance above that point (length of the radius of the bull).
Which to use depends on what you're trying to do. Advocates of combat shooting say you put the FSP tip where you want the bullets to land. Most everyone else advocates 6 o'clock hold. If you're just learning, I would go with 6 o'clock hold, since it is easier to figure out what you're doing wrong.
Basically, though? Center the FSP in the rear sight, superimpose on target, focus on FSP, pull trigger.
Mike