When a player is put on the transferlist, all teams can bid on this player for a period of 24 hours. The amount you bid is hidden, only the teams that already made a bid and the owner of the player can see which teams have made a bid on the player and the order of bids (the highest bid is shown first).
Making a bid always costs you one credit, so consider carefully which players you really want to buy
When the deadline passes, all bids above the asking price are considered. Not just the highest bid. The highest bid has the best chance to win, but the player himself also has influence on the team he goes to. It is more likely you'll win a transfer if you have players from the same country or with the same language as the player you try to buy. Of course it also helps if the player can expect to become an important first team member.
You can always see the current chance to win of your bid on the transfer page of the player. It is possible that the win percentages of all bids don't add up to 100%. There is a chance the player decides he'll rather stay in his current team. In that case, the transfer is canceled.
When 5 or more teams have made a bid, the asking price is automatically increased by 25%. When someone else makes a bid for the new asking price, the deadline for the transfer is reset to 24 hours after that bid. All previous bids are then removed.
From the fourth round, the number of bids needed to proceed to the next round is doubled each round. In round 4, 10 bids are allowed. In round 5, 20 bids etc. There is no maximum to the number of rounds.
It's also possible to make a bid lower than the asking price, as long as no bids are made higher or equal to the asking price. If the deadline passes and there are still no bids that match the asking price then the highest bid below that price will be considered. The manager will be given 24 hours to decide whether or not to accept this bid.