To skin up is to roll a joint, using one or more skins (rolling papers). The expression is used throughout most of the stoned part of the English-speaking world, with the exception of North America, where it never seems to have caught on. In Britain, at the time of writing, it is more popular than any of the other synonyms for rolling joints such as 'build a spliff', 'bill up a doobie' or 'wrap up a fat one'. Like 'hurry up,' the phrase 'skin up' can stand as a sentence on its own.
If you want to learn how to skin up, the best way is to get advice from somebody who already has the knack and then practice until you get the hang of it. If you need to, you can read about it in the sprawling Rolling Joints. Alternatively, How to roll a Phat Blunt covers the rolling of blunts - hollowed-out cigars filled with weed.
I notice that www.galatta.com advertise their collection of browser skins with the heading 'Skin up Your Browser'.
Hey, let me skin up with some of that Mozilla shit man...