On the transfer market, you can sell your players or buy more players for your squad. To buy a player, you simply place a bid for him. The offering manager will then receive a notification and can accept or reject your offer.
If you want to sell a player, select him in the transfer market screen via the plus symbol. You can enter your desired price for the player there, as well as the duration for which the player is to be offered on the transfer market. As soon as the player is on the transfer market, START7 will make you an offer for the player after some time. The other managers in your league can also make offers for your player via the transfer market. If you like an offer, you can accept it immediately and the player will then be transferred to your squad.
Further explanations of the transfer logic can be found in the game rules.