When you have found a player you want to buy, offer as much as you can for the player or enough for the club to accept your offer. When it comes to offering the player a contract, click at the very top of the screen where you choose whether he is indespensible to the squad or used in rotation etc. Click at the top of that screen where it says the player's name and then go to the top corner and withdraw your bid for him and straight away approach to buy him again for £0 or however much you want to spend. Then press either back or continue game and it will go back to the offer contract screen and you then just carry on as normal and you get a player for free!