What is the procedure for retirement from the National Guard?

First, don't do anything until you have the "20 year letter" in your hand. I would start now by getting with the S1 Shop and going over my records to make sure that you are getting credit for all your service time. The Army, Army Reserve and National Guard personnel systems aren't integrated very well and it's easy/common to be missing time and points, so getting that fixed is step one. HRC no longer sends out retirement packets before you reach your retirement age, so you will need to contact them to get it. You may be able to do that online now, but that wasn't available 12 years ago. They want you start this process about 9 months out, but realistically, all that happens if you don't you will have to wait a bit for your first check.
Never had the brief, no idea what it involves.