Ok so you were able to get the nut off of the Delta 622 or other older Delta single handle tub and shower faucet. If not, Please go back here With the nut off , the ball and other parts just pull out then you can just set them on the side, many times a ball can be cleaned up and re used, but if the ball needs to be replaced, please use genuine Delta replacement parts, after market parts really suck.
You can buy kits that have everything you need with out the ball and you can buy kits that include the ball, sometimes the old ball will look perfect, but will still leak, if this happens just replace the ball, Note: There are 2 different balls used in old Delta single handle faucets Please see the following images.
Please note the thicker shaft, looking at it straight on it has a diamond shape. If your ball looks like this please continue following the instructions on this page. Also if you have a sink faucet with this type of ball, these instructions will work for that too.