Everyone sets up a team with a certain amount of money, abit like the cap in the NFL (Seeing as though you pointed out American football)
Then during each round a certain amount of players will be put up for bidding, you then send in your bids in private and wait untill the round ends. This then goes on for a set amount of rounds with the aim being for you the get the best team possible with what money you have available.
If you go over the money cap then you miss out on the next round of bidding or face another penalty in some way. You can either sell back players for a set % or sell them to others.
Once all the rounds are done usually a league of some sort is set up and the winners get prize money, the winner being the one with the most prize money after a set period.
They pretty much all follow the same process although people tend to do theirs slightly differently depending on the outcome they want.