I currently use XAMPP with good success (and was developing pre-OS X so have done quite a few different setups over the years, most of which I now forget). I know a lot of people use MAMP as well, which I think keeps things like httpd.conf in their default location rather than within the XAMPP application itself, but in the end I don’t think it matters.
In a nutshell what you should do is install XAMPP and get that running (can’t remember the steps but it should be pretty straight forward). You’ll need to modify the httpd.conf file to point to the directory you want to be the root folder of your website (I keep my sites in /Library/Webserver/Documents just to keep things like the default OS X install, but you could really put it/them anywhere). httpd.conf is located in the etc folder within the xampp folder.
You’ll need to download your site files from the live server and stick them wherever you have indicated in the httpd.conf file. You’ll then need to import a copy of the database to your MySQL on your machine. I have a copy of phpMyAdmin on my machine that I use, but you could also use a variety of native OS X MySQL front-end applications to do it (haven’t used them in a few years so not sure what’s out there and good).
At that point you’re pretty much done. Depending on your local environment vs your remote one you might be done, or you might need to modify the config.php EE file on your local copy to override the username/password or certain paths.
That’s it in a nutshell. If you haven’t done it before it might take some experimentation, but the reward is pretty obvious and once you get used to it, it’s pretty easy.