I was not here for 5 years and so I do not have any clue how this works to get them. Is it random which skin you get or can you choose before which one you want? Do I have to buy anything before or prepare something in my inventory or just go and zap?

Euclid's laser has an option during October where you can choose to zap yourself instead of pets.

If you go to Euclid's and click the option higher up on the page, you'll get a random skin (links are in the sidebar of the news page). However, there's a more expensive option below that one where if you pay extra SP and tokens, you're guaranteed to get a skin you haven't gotten before, so it's up to you regarding how you want to go about getting skins.

All you need are Wizard Tokens, which can be obtained by completing Wizard Quests.

Thanks for your answer. I was hoping we could choose just the ones we like.

That, we can't do yet. Sadly!

It sorta defeats the idea of Mad Science if you can actually choose. Then it's just science.