If a person falls at terminal velocity, and tries to steer himself with his limbs, what is the maximum lift to drag ratio he can achieve, and what position would that be in?
I'm an ex skydiver. It's a position known in skydiving as a "Flat Track", and is more or less the same configuration as a ski jumper takes. Legs together (ideally), bent forward at the hips slightly or flat, arms at the sides, palms flat. You're trying to turn your body into a "lifting body" type aircraft.
In skydiving videos, it's the position you see jumpers taking to get away from each other when it's time to deploy their parachutes and they need to cover a lot of ground. There is another position called a "Delta Track" where you keep your legs apart and relaxed. Horizontal speed is about half of a flat track.
The horizontal velocity achievable while flat tracking is about 60 mph (making it quite a dangerous maneuver near others if you don't know what you're doing).
With a vertical terminal velocity of about 120 mph, which drops to around 80-90 mph while tracking, this makes the unenhanced human body's L/D while tracking, at 50-60 mph horizontally, at about 0.6/1 to 0.7/1. Adding a Wingsuit improves the L/D to better than 1/1, maybe approaching 2/1.
Everything you wanted to know about tracking here.