First cut or peel off the old grips, which may or may not be straightforward depending on how long they’ve been on. With steel shafts you can be relatively ‘aggressive’ with the knife, always making sure to work the blade away from you not towards you. (You may find it easiest to do this with the club secured in the vice).
With graphite shafts, you must proceed more carefully to avoid damaging them. If you’re lucky, a careful incision at the narrower end of the grip may pave the way to it peeling off easily, but sometimes it will be a painstaking process that you have to carefully repeat as you pick off all the remnants of old grip and tape.
Dab the cloth in White Spirit and rub it up and down the shaft where the old grip was to clean off the final bits.