Two websites, one server

Hi there,

First, I would like to thank all the people that will be willing to help me in any way; I’ll try and return this favor to other users.

This here is my first post on WP forums as I so far managed to get my WP up and running without a hitch, I do thank WP for the codex(s) and documentation they provided, it helped a lot. I am running into a problem though and I have looked for information but all I could find wasn’t clear enough to my taste.

Here is the problem:

I have one website that works perfectly well and I am running it on its own directory (mysite.com/site1 while the URL being mysite.com), with plugins, a theme I created, etc. I would like to create a second website now. This second website can be using the same WP install, I do not mind. But, and a big one at that, it has to be a different domain (understand not a subdomain: sub.mysite.com, nor a different path mysite.com/site2), from what I read on Multisite Network, MU, etc. it is possible to share a single WP installation and database with multiple websites but so far what I have seen only refers to subdomains or different paths not two different domain name.
So if one of you dear helper out there could tell me how to do something like that ?

To sum it up :

Run one website at : http://www.mysite1.com of its own directory (www.mysite1.com/wpinstall1/ for example), then run a second website, on the same server, with a different domain name : http://www.mysite2.com of its own directory (www.mysite2.com/wpinstall2/). If they can’t be in their own directories it’s okay, I just find it cleaner that way.
PS : I get around well with HTML & CSS, can mess around with PHP or jQuery or even Javascript. So I’m not a complete newbie either.

If you have any questions, any recommendations, etc. Feel free (yes, free !) to ask or write it down 🙂

PS : I get around well with HTML & CSS, can mess around with PHP, jQuery or even Javascript but not to the extreme.