The short version:
- open Vegas
- in the Explorer tool window (large lower left panel) navigate to the captured video file (I assume you know how to get video to your computer).
- drag the file into the timeline window, Vegas will create video and audio tracks for you
- scrub (move current position while watching video in preview) to the start of commercial
- press 'S' on keyboard (Split command)
- find the end of commercial
- press 'S' again to split
- the area between splits is commercial
- make sure auto-ripple button in the toolbar is pressed
- click on/highlight area between splits, use Ctrl to highlight both video and audio parts)
- press Delete button - that deletes the selected area and joins parts before and after the commercial
Repeat with all instances of commercials.
When done editing, select Render As... from the File menu and render in desired format.
Of course, to do it right, preserve quality, make cut-outs invisible, you'll need to know more, to try, and learn...