Take in ALL the information you are given at the start of the exercise - don't miss a single word. Missing one crucial fact can completely ruin the lead. This goes for the paper exercises too.
Don't be a shrinking violet. Lead the team. Call on the teams expertese by all means to give you ideas, but the lead is yours so you have to maintain control.
It doesn't matter if you don't even get near completing the task. You can show leadership potential and therefore succeed at OASC even if you barely got half way through a lead.
Leadership is rectifiable by professional training. i.e. you don't have to be a natural leader, just show potential to learn. You can be successful at OASC by not having the best developed leadership, but excel in other areas (eg aptitude)
Like anything, the more you practice/experience you have, the better you get. If you can expose yourself to leadership roles and team leading, then you will fare better at the exercises.