synching audio and video

I have a backing track loaded into Audacity. I have my guitar attached to my PC and record over the backing track (while it plays) and the guitar track works well. I then export this and save it as an MP3. While I am doing this whole thing, I record the video with my Logitech webcam. I have the sound turned off on the Logitech. I then take the logitech video and the audicity audio and bring them both into Microsoft Movie Maker. I synch up the beginning through trial and error. The problem is that I need to synch at at least 5 or 6 places in a 3 minute audio because it seems that the audio playback and the video playback are not aligned. It seems that the audio is a little slow (or is it too fast?). Is there some why to “nudge” the entire audio coming out of Audacity slightly faster or slower so it lines up with the video, better?

The cause of the speed difference that the sound card and video cam are separate devices running with their own clocks without any synchronisation. The problem is unavoidable without buying expensive pro equipment.

Yes you can make the audio in Audacity a little faster or slower, but it will be a bit hit and miss to find the correct amount to change it by. To change the speed, select the entire track and then apply the “Change Speed” effect.
Try changing the speed by 1% and see if that makes it better or worse, then take it from there.