Firstly, you need to turn off the water supply valve under the tank. You then need to make sure you have flushed the toilet after, then widen the tank with the dry sponge. You then will need to get your wrench out to take off the slip nut under the tank.
Then you are able to take off the fill valve with the wrench after. It will benefit you more to buy a new float cup fill valve from your local store because it is more modern and works much better because of the new materials and structure.
When you have your new part you need to read the instructions you receive with this piece to make sure you are pouting it back on correctly. It should be these instructions in reverse but just make sure to read to be sure.
To put the pieces back together, you need your new spud washer over the tailpiece flush valve when placing the tank back on. You need to make sure all of the nuts and bolts are slotting back into place properly before screwing them back on.