2001 Ford focus only starts periodically. The first time it happened, I had it towed to the mechanic. Upon arrival at the shop it started. ?

Charge and load test the battery.  Clean battery posts if battery checks good on load test.  Replace the battery terminals.  Check battery ground.  Clean the starter terminals.  Check for a bad ignition switch.

The starter does not crank the motor it just makes a low kind of a hummmm sound

If it cranks but does not start then god knows - Had a 2000 Focus that refused to start in the driveway, cranked quickly - had it towed to the shop and they started it and brought it in the garage and left it running for an hour - never had a problem with it again- no explanation but while it was there I had the timing belt replaced and water pump because it was in the 110k mile range.

Does it crank but not start? The more info provided, the better the answers. 

Neutral safety switch. Put it in neutral when it doesn't start and see if that helps

You won't get any help if you refuse to tell us if the starter didn't crank the motor over of if the starter worked but the motor wouldn't start.

sounds like an electrical short between the ignition and the starter motor, or between the battery and the ignition, or between the battery and the starter motor, these are hard to find