It varies from bookmaker to bookmaker, but usually when a football game is postponed, the bet is canceled and all stakes are returned to the bettors. This rule applies to most other team sports as well.
Some bookmakers have a time limit within which the game must be played. For example, some of them will cancel the bet only if the match doesn't kick off before midnight of the same night. If the bet was part of a multiple bet, often called an "accumulator" or "parlay", the bet on the postponed match will be canceled but the other bets will still stand and the payout will be adjusted to a lower amount based on the odds. A bet on two teams in an accumulator becomes a single bet when there's a postponement on one of the matches.
These rules also apply to abandoned games, though this is a more complex issue and each bookmaker's rules vary even more on this. With abandoned games, some bets, such as "first goalscorer", will stand. Also, most bookmakers will void all bets if the abandoned game is not resumed within the same calendar date. But some bookies may allow a longer period of time for the game to be resumed before the bet is voided.