I pretty well mirror Gunmans recommendations, but you left out a few things I would like to know before you start.
1) are you going back with standard handguards or going to a free float system, if the answer is free float, is it one piece or two piece?
2) are you reusing your front sight base, if so, measure the diameter of the barrel at the sight base, and compare it to what you have purchased. maybe your new barrel comes with a matching sight base or gas manifold.
3) since your going from a 20' to a 16", this is fundamental, but does your new barrel come with a matching handguard?
4) once you've completed the installation, have the headspace checked, it's usually ok if your using premium parts, but you don't want to fire it to find out.
5) standard front sight base pins are tapered and should only go in one way, and come out one way. If unsure, measure the pins on both sides of the barrel. Drive the pins out from the little end, once again fundamental, but can cause a lot of frustration if done wrong.
Good Luck