Michael Fremer recommends Vinyl Accessories on a Budget

(The above is a couple of years old & Michael recommends the Onzow stylus cleaning 'sticky goo' which costs '60 bucks'.... you could go to a $2 store & try some kids' Goo-Slime (which I don't recommend as I've never tried it!), but you can also use the Magic Eraser (cleaning pad from supermarkets), an inexpensive & tested technique for cleaning a stylus, as below....)

I use a combo of stylus cleaning methods, as Michael does, liquid cleaner + brush, magic eraser now & then only.