How can I play a Blu-ray DVD on my Windows computer? I know I need a new DVD drive, but what else do I need?"
To play a Blu-ray movie on your computer, there are several things you will need in addition to having a Blu-ray drive. Blu-ray requires fairly robust hardware for smooth playback, so you might need to upgrade some components in your computer. Blu-ray also requires software with the right codecs for playing Blu-ray disks. And if you are connecting an external monitor to your computer, your video card needs to be HDCP compliant in order for Blu-ray playback to work.
Software for Blu-ray playback
Software for playing Blu-ray is the easy part. Cyberlink PowerDVD Ultra plays Blu-ray media. It has the bonus of also playing AVCHD camcorder files.

Hardware for Blu-ray playback
As you already pointed out, you need a Blu-ray drive to play Blu-ray discs. You also need to meet additional hardware requirements with your PC. In theory, you simply need a Windows Vista-ready machine, but that won't guarantee a perfect experience. Things are further complicated because in addition to needing a beefy processor and plenty of memory, you need a graphics card with very specific characteristics and monitor with HDCP support.
One helpful advantage of Cyberlink PowerDVD is it ships with a tool to help you figure out what components need upgrading in order to have a great Blu-ray experience on your PC.
HDCP Compliant Graphics Cards
The graphics card needs to be one of the few that support HDCP. Many ATI and Nvidia graphics cards now support HDCP, but you still need to read the specs to make sure yours does.

HDCP Compliant Monitors
Monitor support for HDCP remains the biggest gotcha. Updating to the latest version of your graphics card drivers can solve this for the graphics card, but if your monitor is not HDCP compliant Cyberlink PowerDVD Ultra will either throw and error message or play back with a black screen (which is expected behavior).
The easy solution to the monitor problem is to plug your computer into an HDTV screen over either HDMI or DVI. HDTV screens generally ship with HDCP compliance built-in. Finding a true computer monitor with HDCP support is a little more complicated. I tend to prefer Samsung monitors for most things - I've always had great results with their products. Samsung does a lousy job of documenting HDCP support in their monitors, although I was able to find product specs listing both the 206BW and 226BW models as supporting HDCP. Dell does the best job listing HDCP support, listing this as a feature on virtually every widescreen model in their current product lineup.
The bottom line here is, if you want Blu-ray playback on your PC, you need to read the fine print to make sure the components you buy will do what you need. Many monitors are starting to support HDCP, but there's still a majority that don't, especially at the budget end of the market. Many integrated graphics cards do not ship with HDCP support; the AMD Turion X2 chipset is one key exception. Before you buy, make sure you keep your options open.
Do you shoot videos with a camera or camcorder?