First step, make a protection copy of the show on separate media like a USB stick. If the machine has troubles or Audacity freezes in the middle of production, you don't want to permanently lose everything. Never save a corrected show as the same name as the original and don't use MP3 anywhere until you have to actually post the show. Use WAV for everything.
Drag-select the portion that you want to remove and press the keyboard DEL key.
You can use the spacebar stop and start to play the selection and make sure it's correct. If it's a long selection, do it in steps. Take most of it out the first time and then play what you have left. Then remove more.
The zoom controls are handy.
http://manual.audacityteam.org/o/man/zooming.html
I usually use only three: Zoom into selection
Command-E, Zoom out Full
Command-F and Zoom out a little bit
Command 3.
I don't much like Audacity pulling the timeline view away from me automatically as I edit, so I turn that setting off.
Audacity > Preferences > Tracks > Update...
You probably want to turn that back on for recording.
You can use labels as reminders of where everything is. They're sticky, too, so you can use them to accurately select a passage for deletion, effects or corrections..
http://manual.audacityteam.org/o/man/label_tracks.html
Koz