Make the Connection
There are three ways that your PC can potentially hook up to a HDTV - DVI, HDMI, and Displayport. The first two are the most common, but Displayport is beginning to show up on a few HDTVs. In practice, they all achieve the same goal, and provided that you're simply planning to use an HDTV as a computer display - not as part of a dedicated home theater system - they are virtually identical in performance.
DVI is the most common, and is the mostly likely method you'll choose to connect your HDTV and your computer. All modern day video cards use DVI out, and the majority of HDTVs will accept PC input through a DVI connection. Note I said most, however. Some budget models do not have the capability, so be sure to get the dirt on the HDTV you're thinking of buying.
HDMI is also very common, and is becoming increasingly easy to use now that both AMD and Nvidia are providing full HDMI support with their video cards. In fact, some video cards - mostly those meant for home theatre systems - include a HDMI connection. If there is no HDMI connection, you can buy an adapter that turns the DVI connection into an HDMI connection.
Lastly, there is Displayport. Displayport is being pushed most heavily by Apple. It has some functionality which is supposed to make it easier to use with PCs, but in the situation we're covering here it is unlikely that functionality will come into play. It is simply another way of connecting, and will be the simplest method if you own a new Apple with Displayport.