How does one initiate ground combat in StarDrive?
On a planet where you have troops, right-click the troops in the map window to send them into orbit in assault shuttles.
Those shuttles are generated for free, but have no defenses whatsoever, so don't send them unescorted if you don't already rule the orbitals.
Send the shuttles to the target planet, then once they're in orbit open the planet's combat view (select planet in galaxy map, click the lower button). You can then deploy your troops to the surface from the ground troops tab.