If you simply start Ableton Live and the Machinedrum by pressing their start buttons manually, then any small difference in the internal clocks of the two devices and any time difference in you pressing the buttons will cause problems with synchronization.
The MIDI capabilities of both Ableton and the Machinedrum allow you to use one to control the other by transferring precise clock signals between the two.
By setting up Ableton Live appropriately, connecting a MIDI cable between the MIDI Out port on your soundcard to the MIDI In port on the MD, and making Global settings on the MD to allow it to receive MIDI clock and MIDI transport messages, you will be able simply to press start on Ableton Live and the MD will automatically synchronise its playback with Ableton Live.