I have written up a pretty simple howto I hope on setting up your static home page. You can find it here: http://www.richandstephsipe.com/wordpress/2007/02/12/wordpress-21-static-homepage/.
My blog is setup with WordPress in a non root folder (mine is creatively named /wordpress/) and I have a pre 2.1 pretty standard template (although hacked to beyond recognition) setup and I had no issues.
You shouldn't need an external plugin etc to enable this feature but if you had one active before the 2.1 release to hack the static home page feature you will need to undo this. Also if you have a home.php file I think you need to rename/blow it away because it causes issues.
The biggest gotcha is you must "create" the new page to use as your static homepage using the WordPress-->Write-->Write Page Admin menu and NOT by creating a new .PHP page by hand and manually uploading it to your server. The old hack way to do the static page involved creating another page manually and then hacking it into place but WordPress 2.1 allows you to do this all within the WPAdmin manager without the Ugly Hacks.
To make your new home page look different you will need to create a specific template with the design you want for your home page. Then you need to create (write in WordPress speak) a page using WordPress that you set to use that new template (mine has a blank Content section for that page). You also need to create another page in WordPress to use as your blog page since you now don't have that on your homepage and set that page to use your normal template. Anyways ... I don't want to rehash the longer writeup I did and end up confusing people more.
GATEKeeper: If you don't see the "Front Page" option set as your first one your 2.1 update probably had some issues and you will need to redo it.
If my blog write up isn't clear throw down a comment on the post and I will try to make it more clear.
The issue I had and many others now are facing is the old hacky way to do it is getting mixed up into the new 2.1 way and confusing people. When you Google Static Home Page you get all the hacks and when you look it up on the WordPress support boards you get hacks mixed up with the now correct way to do it and it is hard to figure it all out.