Depends, it's complicated
the player's agent gets a lot
the club gets some, and in some cases previous clubs get a sell on fee, which helps a little club when they sell a player to a premiership club, when then sell him on for silly money, for example Southampton got some money when Bale went to Real Madrid from Spurs.
The player may or may not get them. If the player is mid contract, and asks for a transfer, then he's not entitled to transfer fee money, however, if it's all done above board properly, and team A approaches team B, and they agree to sell player, then he gets money.
I'm pretty sure brown envelopes are involved so players get money no matter what though
