If you are new to this it can be hard understanding Arbitration when doing the budget, so it better to have an understanding first. Arbitration can be one of the most costly things with your team. Arb Eligible players have a minimum of 3 years of ML experience and they are ready to cash in on a big payday. Their cost is handled about the same way that FA's are priced, just the percentages are broken down differently. Whether to sign an Arb player is up to you, there can be many reasons to sign or not sign a player. If you do not want to sign an Arb player, then release him and he will become a FA. He will not sign a contract with you once you do that and there will be no compensation picks either. Also you must release the player before the last cycle of arbitration or he will be signed at least 70% of asking price by default.
You can also trade the player, it is best to have that set up in first cycle after budget is set because there is not enough time for the trade to go through before the arbitration cycles end.
You have several options with an Arb player. You can offer a 1 year deal at his asking price. You can sign him long term at his asking price. You can offer a deal and arbitrate.
When you display the arbitration screen, the amount listed there is for a 1 year deal. After you have offered a 1 year twice, he may not accept a third and opt for FA instead, so be careful there. If you click on long term it will show what he desires in a long term contract.
When the arbitration cycle starts you must make up your mind what you are going to do. If you do nothing, the AI will and that could be financially disastrous as it will use up the Player Payroll then start taking money from other areas to make sure they are paid.
If you want to sign the player to his long term contract demands, it is best to do so during the resign FA period. Simply click on long term and submit offer. He will either accept or not. I never had one not accept, well there is an exception to that and it deals with AI and an amount ending in 999 etc. If that happens, just add $1 to $3 to the amount in the first year and it will accept (it can't divide certain amounts evenly and it sees it as not meeting demands).
If you wait until the arb cycles you can still meet his long term demands by clicking on the long term link in the instructions and click arbitrate. But if you are going to do that, you should have already done it in my opinion. Of course there are reasons for doing it that way, like trying for a cheaper price.
If you want to offer a long term contract less than he demands, do so by clicking on the long term link in the instructions. You can then make an offer less than he is demanding but be reasonable. Then you click arbitrate. You will either win or lose the case. If you lose the case, the cost will either be his demands, somewhere between the two or in some instances substantially more than his original demands.
1 Year Deal:
Just click arbitrate and a box will appear for an amount to offer. I usually put in more than he wants (not by much), but either it ignores the amount or it doesn't want the commas or something. Then click submit and it will arbitrate. I have always had a reply of player wins case for the amount he requested.