How does the transfermarket work? Example:

A player with a market value (MW) of 100,000 is offered on the market. The initial bid is 80% of the MW. In this case at 80,000.
You can choose your maximum bid, for instance 150,000, in the case that you have enough funds available.

Your bid will be publicly visible at 81,000. If another manager bids on the same player, your bid increases automatically by 1000 until your maximum bid of 150,000 is reached.
You can always increase your maximum bid, but you cannot withdraw from it.

If you are selling a player (in the squad screen), the selling price amounts to 80% of the market value. In this example, you would receive 80,000 for this player - if you have not trained him in the meantime. Afterwards, the player will disappear from the game and he will not be available for other teams.