I am actually studying for the ASVAB right now, as well, although I have previous experience with geometry. You could probably start him off with what teachers call realia--using real, hands-on things. He would probably learn better by doing than by reading. So assess his basic math skills (is he okay with adding, subtracting, multiplication, etc) because that is needed in geometry. Then teach him the vocabulary needed for geometry while showing real-life situations for him to learn from. After the basics are learned (probably about a week or two, maybe a little longer, depending on how often you work with him) you can start to do the math formulas.
I wish you and your friend luck. A high ASVAB score is really needed to get many options for the military. But just remind him that a miminum of 32 is needed for enlistment for the marines, just so it can take the pressure off of him. Good luck!