Downloading the VoD
I use a firefox extension named DownloadHelper because it's something I already had for downloading youtube videos. You browse to the vod you want to download, click play and let it start buffering and then click the extension icon and download the .flv - it downloads like any other ordinary file. You can close the page at this point and let it go.
Another option I found just while googling is a website with a tool called Twitch TV Video Downloader. I haven't tried it personally to see how it works but it seems pretty straight forward you just paste the URL for the vod you want to retrieve.
Extracting the .flv
Now that you have the .flv downloaded you can most likely play it in a player like VLC already, but there will most likely be issues with the audio as most twitch recordings use .spx and it doesn't seem to play well with VLC/Vegas. I use a small tool called FLV Extract. It's really easy to use - after you extract the zip, open up FLVExtract.exe and you'll see a window like this:
1) Open up FLVExtract.exe:
2) Click the .flv file you downloaded and drag it onto the above window.
Something like should appear now. If it seems like it isn't doing anything at first, don't freak out - it might just take a few minutes depending on how big the file is. I just downloaded a VoD that was 2 hours long (about 1 GB in file size) and it took my laptop a couple minutes to take care of it.
True Frame Rate: You might want to take note of this number for the next step (which may be optional).
Converting these newly extracted files
You should have a few new files available in the same directory as your .flv - .264 is your video file, .spx is your audio file. You may be able to just import the .264 file into Vegas, but I haven't had much success with this - for me it's resulted in VERY SLOW wait times and Vegas freezing up but it could be a result of me using a pretty crappy laptop. If you have this problem, see next:
Putting the video into an .mp4 container
I've had a lot less trouble with the video file when I convert it to an .mp4. The slow loading times and freezing that I had occuring with the raw .264 file seem to be gone completely after I did this, so you might give it a shot if you are having problems also. For this step I use a program called Yamb (Yet Another Mp4Box UI), which is also freeware, and it's relatively simple.
1) Double click this first available option (create an mp4 file)
2) Click the "Add" button on the right side and browse to your .264 file
3) Select the .264 file in the list and click "Properties"
This is where you want to input your True Frame Rate from before. Typically this is going to be ~25. Adding a random higher number isn't going to improve your quality or anything, it's just going to make it seem sped up when you go to edit it.
4) Click Next and let it do magic.
Converting .spx to .mp3
In my experience Vegas really doesn't like .spx audio format for some reason. I tried a bunch of different trial programs that ended up expiring after a few days or had crappy limitations like only letting you use a portion of the source. I ended up finding out you can just use VLC media player (all around amazing player compared to Windows media player that most people have anyways) to convert the file pretty easily, but it was a little slow for me.
1) Open VLC Media Player and press CTRL+R or go to File > Convert / Save.
2) Go to "Add" and find your .spx file, then at the bottom click the dropdown arrow and go to "Convert" or press ALT-C.
3) Click "Browse" next to Destination file, browse to whatever folder you've been working in and name it whatever you want .mp3. Change the profile being used to Audio - MP3.
Everything should be good to go now, just click Start and let it work. It should have a progress bar going across the screen as it normally would if it were playing back a song or a movie, but I haven't gotten an estimated time function to work yet.
Import your files into Vegas
File > Import > Media - find your new .mp4 and .mp3 files and they should be compatible for editing now.