A body recomp is something that pretty much happens naturally as you (1) build muscle and (2) eat in a small calorie deficit. Just do the right thing to maximize its effectiveness and that's about it. I would also suggest that you track your progress. Seeing what you're doing on a regular basis is going to help you improve. You should take pictures because just seeing the progress you're making is going to help you stay motivated.
It also gives you a healthy sense of competition with your past self. Just remember that all of this is going to take a lot of time so be patient with yourself. The process of turning your body from fat to lean(er) is a lot of fun. If you're pushing yourself in the gym three days a week and trying to improve your diet, you're going to see results.