As others have said, once you buy a non-refundable fare, that money will (barring IRROPS or some other unusual circumstance) not be refunded to your original method of payment. Unless you are on a Basic Economy (fare class N) fare, you can pay the applicable change fee and apply the residual value towards a future ticket on United for up to 1 year from the original date of issuance. You must cancel the flight before departure of the first leg (or before departure of the next leg if you are in the middle of the trip) to retain value. You should retain the ticket number and confirmation information to be able to apply this value to a future ticket. You will pay the change fee when you utilize the residual value in the future, not at the time of cancellation (to my knowledge). I am fairly certain this is not possible to do online and must be done by calling United directly.

Even if you change your flight, the amount you bought as a non-refundable ticket will stay non-refundable. The new fare rules will apply to any *extra* money you give United, but the original money will have the same refundability of the original ticket - i.e. not under normal circumstances.