Absolutely the best way. Get some coffee filters - they are dust and lint free if taken directly from package. The best lint free cloth you can get.
Find some sylene based solvent such as Goof Off! or 99% pure Isopropyl allcohol. I usually use the Good Off first which tears through gobs of thermal compund. Be care not to be messy with it. I use the Goof Off! to get most of the compound off, then use alcohol to give it a fine cleaning. Then let it evaporate.
If you are going to reapply thermal compound to the cpu core or chip cap, apply it to the heatsink first; about the size of a tiny pea. Like a big BB. Get a credit card and take a dab. Use this dab to spread it evenly acroos the cpu. Keep a nice sized gob on the heatsink and apply it like that. It will spread out from the pressure.
When you first apply new compund let it cure a bit (some say you don;t have to) which I do. And for the first month. Do not let your PC run non-stop if you can. Give it a rest once in a while so the compound can "break in."
Good luck and hope this helps.