Not sure I agree with letting the bike steer itself, but I've only ridden track at Calshott which is apparently a shorter track so tighter turns? There I was told to put weight on the bar with my left (inside) hand and it helped a lot.
If it's your first track session then pace yourself, my first couple I was almost throwing up half way through
Also, if you're riding in a peloton/train (right word?) then trust that the bloke in front won't slow down as if he does you're both toast. Likewise, if you have someone on your wheel don't slow down.