When you buy a player he will automatically be given a three day contract. Within these three days you must renew his contract if you want to keep him. If you do not renew his contract, the player will leave your club shortly after the contract has expired. Your club will get the credits if he is sold after his contract expires, unless the player has trained less than five times.
By renewing a players contract he will ask for a specific amount of days and a demand for a wage that he finds to be optimal. It is your job as a manager to determine if that is fair, or if you want to negotiate the length of the agreement.
Besides negotiating the length, you have the ability to negotiate the wage as well. This does involve some risk though. You can end up paying more than initially required, so be careful.
If your balance is below minus 1,000,000 Credits, your board will not allow you to renew contracts on players that require a wage. In this situation your only way out is to sell players until you have more than -1.000.000 Credits to keep the remaining players.
If the club is less than 60 days old, you are not allowed to go below 0 Credits by renewing contracts. This is to protect new clubs from a bottomless debt, that they cannot get out of.