|The capture card you buy will probably have some software you'll use, but there are other programs out there. If you don't want to mess with installing new programs, I think most versions of Win7 have built-in software.|
Capturing video, on the other hand, is a bit more difficult. You'll probably need one of the VirtualDub variants (assuming VDub can handle HDMI video), and a fast lossless or semi-lossless codec. I'm sure the Doom9.org forums can help you on both counts better than I could.
Any editing you do should be done with this raw capture. (Especially if you pick a lossless codec that doesn't have keyframes.) I don't know of any good video editors; I used AVS for light editing, which I do not recommend. It's great if you want to process batch jobs or you're a programmer, but it should be otherwise avoided.
As for post processing, you'll want to encode the video as H.264. Pick the encoder that works best for you; they all use the x264 library anyways, so the only difference is the GUI.
For audio, encode that as an MP3. I like the LAME based ones.
Your container? MP4 or FLV if you want to upload it to a video site. Because this encoding takes the most time, I suggest you make a few test captures, one to two minutes in length. That'll keep the encoding time down short enough while you play with the encoding settings. Just make sure to check for audio / video desync when you start making longer videos.
Once you get all THAT worked out, you're more or less ready to go. Just make sure your PC is doing nothing else while recording, and keep an eye on your free HDD space. (Remember, you need enough for both the raw capture and the final encode.)
If you find the latency too high on your PC, you would be better served with a HDMI slitter and a second video monitor than any PC upgrade. If the video or audio is too choppy, or you get dropped frames in the captures, you'll need to either free more resources for the capture equipment, or a new PC.