This site is made with HTML5, but without a few little extras, the styling and layout would break in all except the most up-to-date browsers. For example, in all versions of IE (except IE 9, which is still currently in beta) the CSS applied to new HTML5 tags would not work, and in Firefox 3.6, the layout would not look the same as in Chrome.
Here is a quick list of things you'll need to get around these problems. None of them are hard to apply, and all the really hard work has been done by other people. Bonus!
1. The New Doctype
From the W3C's working draft of HTML5, finally a doctype you can remember! Without the doctype, certain browsers will enter quirks mode (in order to maintain backwards compatibility for pages designed with standards that are not the W3C's) and you have basically no chance of getting you web page to look right.
2. A Tag Reference
Knowledge is power, and so W3Schools HTML5 tag reference is a good place to start. How you interpret which tag is right for which part of your site is more or less up to you, but remember, the tags are to be used to give semantic meaning or context to the information in your page. Some are more obvious to apply than others.
At this point, you site will probably work with Safari, Opera and Chrome. So yeah, none of the big boys. The next two points include code that you can apply to your page, and are included (with loads of other stuff) in the fantastic HTML5 boilerplate, but if you want a simpler solution you can just include them yourself.
3. A CSS Reset
As mentioned before, even Firefox has trouble with HTML5; the new tags are inline elements by default, so applying
display: block to them will fix most of the problems. A good CSS reset will do this and more, and is a great base from which to start coding.
4. The HTML5 Shiv
Now you've got your site working in modern browsers, you need to give IE 6-8 a kick up the backside. These versions of IE do not recognise the new tags at all, and will do all sorts of strange things with them (as they would for any other tag they do not recognise). For this site, IE will decide to push all the content out of the header and into the white content section below. Very annoying.
However, if I include Remy Sharp's (and Jon Neal's, with a little help from Sjoerd Visscher) brilliant HTML5 Shiv (or is it shim?), all my troubles are over. What this does is inform your browser that the world has moved on, and that other versions of HTML have come into being. You're basically having to tell a browser how to do its job, and creating the element in the browser's DOM.
<!--[if lt IE 9]> <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script> <![endif]-->
All done. Now go! Make a site in HTML5! Or HTML. Or whatever the cool kids are calling it these days.