I can't get my domain and hosting to work with eachother...

Yes, I'm a huge newb when it comes to this stuff. So I purchased Russian 2xr.ru hosting. I set mywebsite.com as my domain at the hosting site, and then I registered the nameservers (ns1.2x4hosting.ru, ns2.2x4hosting.ru) with mywebsite.com, a domain I bought from namecheap.

Isn't this all I need to do? Or am I missing something? I've done it before but I can't remember what I did and half of my hosting is in Russian.

Setting the nameservers for your domain simply tells people's computers which servers to query to find out which IP your site is available at. You need to set up the other end, which is the mapping of mywebsite.com to the actual IP address it's available at.

I'm not sure how 2x4's admin panel handles that, so I can't help.

Once you have setup the name servers it can take up to 72 hours for the domain to propagate. After that if it is still not working contact the host. Most hosts will give a temp url to upload stuff to your site while your domain is propagating