If you click your player's name you reach his personal page. In this page there is a "sell" option. You can decide on a starting price, give an order to sell, confirm the selling and from that point it will be available in the transfer list for other managers to bid and buy.
Selling a player does not cost you any price - not in money and not in gameshape or so. The only price is that if you buy and sell a lot, your fans will be less satisfied (being afraid that you are going to sell the team's stars).
The transfer market works in an auction system - highest bid wins.
There is a deadline and it is a flexible one - if someone makes a bid just before the deadline - deadline moves to 3 minutes after the last bid