I use either bits of fleece of old bits of towel. I either use them seperately but i prefer to sew them together on the sewing machine. I use the towel side for the more 'grubbier' side of businness iykwim
and the fleece side for just wiping.
I also have just fleece bits for drying off afterwards.
Wetting them: If I am in the house I use a bowl with just water in. If I am out I take a small handbag size spray bottle and spray the wipe
They don't need to be perfect just odd ends will do