Basically, it goes like this:
You make a bid in the main stage (before the deadline reaches zero). If you are the only bidder, you win. If not (and 9 out of 10 times this will happen), you go into knockout stages where those who bid a token before the deadline will bid amongst themselves for the player in each knockout stage (The time is decreased to 30 seconds after the first stage, then 20 seconds after the second stage and carries on from there after). This will continue until the player is eventually sold.
However, some bids (which people have posted screenshots of) can go on a ridiculous amount of rounds, while others can finish quite early on. Obviously, you'd need to use some common sense as well (mainly when to stop bidding if it continues and compared to the amount of tokens you have available).
While others can give you better tips, one I can give is look at those you are bidding against. If you see a team that has a vastly superior quality to you team wise, don't bother bidding as they are most likely people with plenty of tokens available.