Absolute must-haves in any briefing (my opinion):

1) navaid and frequency
2) final approach course
3) final approach point
4) step downs before MDA/DA
5) MAP and missed procedure.

Conveniently enough, this is pretty much the order they are in on the plate itself (Jepp anyway, I haven't looked at FAA charts in a while). So, the way we typically brief the approach is just read left to right, top to bottom on the approach plate and set things up as you go. Note anything that can't be set up yet because you're using it to navigate now, and be sure you fix it later.

My advice would be to be careful not to over-brief. If you try to keep too many things floating around in your head, you're going to have a lot of things you've forgotten rather than a few things you remember. What you should brief are the things that are important for you to have in the front of your mind while you are doing more important things such as flying the airplane down to MDA/DA.

I wouldn't necessarily brief too much about the approach before the FAF, for example. This you can usually read ahead a few steps and be ok. If there is something especially bizarre about the approach in the initial/intermediate segments though, go ahead and brief it. Like if you are supposed to do a barrel roll at 8DME or something.

Other than that, you should be able to fly the approach from the FAF to the first minute or so of the missed procedure without looking at the plate. Not that you can't or shouldn't look at the plate here to confirm things, but the last thing you want to be doing a minute after starting to descend from the FAF is going "What was MDA again?"

I hope this was helpful...