Wordpress Multisite Support (& Multiple Domains if Possible)

Hello,

I installed wordpress on a subdoimain with the intent of creating multiple websites under the following domain structure:

Wordpress installation: wordpress.alexsobiek.com
Site 1: site1.alexsobiek.com
Site 2: site2.alexsobiek.com

and so on.

However, I haven't found a good solution to this so far. I've been reading around the forums and I saw a couple of posts but don't quite understand them. Wordpress includes rewrite code for the .htaccess of the main installation domain (wordpress.alexsobiek.com) but that creates subdomains (that don't even work) such as site1.wordpress.alexsobiek.com. I'm wondering if anyone has a solution or any ideas of what I could do. My main site, alexsobiek.com is not wordpress but if I have to switch it to make all of this work, I'm open to that option. 

Thanks!