In a very basic form, it would look a bit like this:
avconv -i inputfile.mov -c:v libx264 outputfile.mp4
This will only work if you compiled avconv with libx264 support - you can see here on how to do that.
If you're not that concerned about codecs and just need an ".mp4" file, you can also run this:
avconv -i inputfile.mov -c copy outputfile.mp4
This will copy all codec information from the .mov container and place it into the .mp4 container file.
Just as a note, avconv is a fork of ffmpeg, many of the switches for ffmpeg will work for avconv (if that helps your search for answers)