For removing thermal paste, either a coffee filter or some other lint free cloth. A paper towel will work if there's nothing else but it's not lint free and can leave little bits of material behind. Try to wipe off the bulk of whatever is still on the cpu then use a lint free cloth or even a q-tip moistened with rubbing (isopropyl) alcohol. That will clear off any residue and it dries fast (evaporates).
As far as applying thermal compound, everyone has their own way. A small pea sized dab in the middle, a rice grain sized small line vertically down the middle or an 'X' shape. If using the 'X' shape just remember that you're adding two lines so they need to be a bit thinner than if using a single line down the middle so you don't apply...