There are two different issues here. First, Moodle runs on the server, not on your machine. Moodle delivers content to your web browser from the server. In most cases if Moodle is running slow, it is because folks are trying to run it from a bargain price hosting company that has 100s of other sites on the same server (that is how folks who give you 1GB for $9.99/month make money).
This is often a bad idea for any sort of production site. Remember, Moodle is a course management system, it compares to WebCT and Blackboard, which cost thousands of dollars per year just to use, and they are generally set up on their own server, with very high requirements. Blackboard doesn't even let you run any other application on the server it runs on.
While you can run few classes off of a low cost hosted site, you have to shop carefully to find a hosting company that knows what they are doing, many will sell you the space and install Moodle, but they won't give you enough processing power and RAM on the server to run Moodle properly. Nicole Hansen posted some information here about her hosting company, which I gather runs fine for her uses and even sends some $ back to Moodle, so you might want to look into changing hosting companies to one that will give you the right set up on the server to run Moodle properly. More
http://moodle.org/mod/forum/discuss.php?d=29285 (I'm looking for an external company for a small Moodle side project, so I'm defintly going to give these folks a try
--thanks for mentioning them Nicole!
For large scale installations, with thousands of users, I recommend a dedicated server with at least 3Ghz processor and 2GB of RAM, more processors, more RAM, a separate database server, a cluster are a good idea as you run into the upper thousands of users and into the 10s of thousands.
The system requirements on the client (the users) side are modest, you just need a modern browser and a system that can run it. Probably you'll want 200+Mhz if you are running Windows or MacOS (and if you are running MacOS 9, you have to run Mozilla 1.3.1 unless you know how to fix your theme). But if you can load a complicated site like say slashdot.org on your computer without it taking to long, then the problem is almost certainly with your hosting company (though see below about possibly overloaded home pages).
If you have a good server and Moodle is slow, the second issue is that if you have an overloaded home page, of course this can slow things down as the server has to deliver the content from the home page to your users web browser. I've seen some Moodle home pages with several megabytes worth of pictures, flash, etc. on the home page, which will definitely slow the site down, especially for modem users. Moodle makes it very easy to post lots of content, but it doesn't optimize the pictures, audio, etc. So that is another thing to check.
But most of the time the problem is with a cheap or poorly run hosting company.
