The same way you place any other bet.
There is someone setting the odds (the bookmaker) and you give him your money up front. There's a huge element of trust here that the bookie will record who bet, how much, on what result and at what odds.
Depending on the movie or show, you may or may not see the bet being recorded....but it almost certainly is...the bookie will probably have a boss!
If your chosen fighter wins, you go to the bookie and collect your winnings.
Of course, given the (often) illegality of bookmaking and especially on illegal fights you have to hope the bookie will be there to pay you off...or has the money to do so if they got the odds wrong.