To unlock the ability to make wagers you first need to complete the challenge that requires you to earn 2,000 dollars. After doing that challenge you can then bet wagers in gang wars. You also need to be level 4 in order to unlock the full playlist which contains gang wars, which is the mode where you can place a wager.
Now go play a game of gang wars and before each round starts you need to press "X" so the see the available bets you can place. Each wager costs $100. The amount of money paid for each win is dependant on the players's postion, score and other factors.
So after pressing X before the round starts the game will give you a screen with 3 players you can bet with (sometimes you can bet on yourself). It will also give you the criteria for which you need to win the bet like "Most melee kills" or "first one to get a kill". Just meet the criteria before your opponent and you will win the bet.
Betting on yourself is an easy way to go, so if you see yourself on that list of 3, take the bet.