MartiniDelini

The easiest method would be to get a wifi card for your computer. 
Bridging can be problematic, I tried to do that for a while and it's annoying to deal with. 
Something that's more expensive but does what you're looking to do is get an access point (make sure it's capable of doing this before buying) that you can put into wireless bridge mode, Many access points will have a few ports out allowing you to plug in your computer and your laptop to make networking them fairly easy. If you have the budget for it, get a Ubiquiti AC access point and a decent gigabit switch. This is a little more setup but it's stable and allows for a full wired connection between your laptop and desktop.

share laptop's internet:
connect laptop to desktop with cable.
On laptop: bridge wifi to ethernet
 
direct desktop - wifi connection:
buy USB or PCIe wifi card
connect laptop to desktop with cable for fast connection between those (you will have to manually set ip's, Linus does this in one of his video's)
 
I suppose you run windows on both, so I can't give you exact instructions.
If you run Linux on at least one, It would be easier, and I can give you step by step instructions