In answer to the original question, you can either create a betting account with some site (and deposit your BTC to bet) or there's a lightweight model where you bet on a proposition by transferring your BTC to a nominated (unique) address. If you win, your winnings get credited on the return address.

The latter model provides anonymity and ensures that your details (and your wallet) cannot be ransacked. We take this approach in http://betoneurovision.com