There are lots of ways of setting up a prediction market, here is the simplest: Imagine that it will soon be objectively determined whether X=1 or X=0. There would be a separate section in LessWrong for karma bets. In this section you could offer a bet, i.e. I give you 20 karma if X=1 and you give me 10 karma if X=0. One would click on this bet to accept. The sum total of all your karma bets couldn't, at the time you made a bet, exceed your total karma.

An administrator would have to decide what events could be bet on, and which side won each bet. I would be happy to do this, although of course Robin Hanson would be the best person for this job. I don't have the skills to help you with the programming.