There are lots of ways to change direction on the skin track. Ideally you don’t need a lot of uphill skill, and if you are careful, and a bit lucky, you can set an easy to follow skin track that never requires a sharp switchback. In that case, all you need to know is how to sniff out the low angle dips on a slope and strategically link them so that all you ever need to so is a simple, 3-to-4 step change in direction that the AMGA calls the A-V-A turn. Depending on how you initiate it, it might be a V-A-V turn. All you do is progressively change the alignment of your skis to form an A, then a V, then an A, until you have changed direction.
In theory this is all you need to know about changing direction while making switchbacks up a slope. In practice you will need a lot of luck to be able to rely on this direction changing technique exclusively. Even so, it is presented here for the record to illustrate this specific turn requiring the most rudimentary skinning skills.