You need to first install the software on your computer, register the unit with Garmin, and do any firmware updates that it might need. The unit is probably turning off because the battery is low. I strongly suggest hardwiring it to your battery, which is very simple. Route the wire down the steering head and behind the left front side panel along the trellis frame, and then to the wire bundle than runs in the channel under the seat, to the back where the battery is. You should need anything more than a handfull of wire ties, a couple of allen wrenches for the side panel and wire keepers under the seat, and a Phillips screwdriver to attach the leads to the battery. Shouldn't take you more than fifteen minutes.
Did you use the mount that came with the Zumo? If so, you might want to check out the Tech-Mount low-profile handlebar mount, which works very well on the HM.