I'm guessing @jaablake would like to export a gpx or tcx file from a course he's drawn on Garmin Connect. Although you can export an activity, Garmin doesn't provide the ability to export a course you've drawn. That's why I only use ridewithgps.com for course creation. RwGPS also creates decent cue sheets from routes you've drawn.
Garmin Connect doesn't provide a button to click to get the course, but you can easily do it with a little bit of url hackery. Have a look at this post.