In games like Blackjack, Roulette, Craps and Baccarat just press with your right mouse button on the chips you wish to remove. In Roulette you can also click on the 'Clear Bet' button to remove your entire bets from the table.
In Slots and Video poker, just press the 'Cash out' button to remove your coins from the machine back to your balance. If other coins remain in the machine, don't worry, they will automatically return to your balance once you exit the game.
Once you hit 'Bet' or 'Deal', your bet is locked in and cannot be refunded.