There are two main ways to move land units in Hearts of Iron III. Strategic redeployment is a fast and cheap way to move people away from front lines. The real world equivalent is that it is cheaper and faster to put tanks and soldiers on trains than it is to have them march and drive. Continuing this notion, the speed of redeployment depends on the Infrastructure ratings of the provinces being crossed.
The draw back is you don’t want your infantry to show up in combat on a train and start lining up to get their rifles from the baggage car. This is reflected by the troops taking an organization penalty that grows over time as they are redeploying (they take similar penalties when loaded on ships or planes). Simple movement uses more supplies and fuel, and is slower, relying on the unit’s movement speed, but doesn’t hurt organization on its own. Marching through a hot, steamy, pathless jungle will carry its own penalties, though.
To order a unit to move to or attack a nearby province, you just select the unit and right click where you want to go. We have some mountain infantry, the Corps Expeditionnaire hanging out in Marseilles. If they were garrison type infantry, I might be tempted to leave them there, but these Alpine specialists would best be used in, you guessed it, the Alps. I will drag a box around the unit stack in Marseilles, trying not to include the naval or air base.
I will get a list of all the land units in the unit panel, and depending on my clicking skills, air and naval units. Use the little Xs to remove any air and naval units, and the HQ as well, since we don’t want to move that right to the front. Just right clicking in the target province, Briancon, will get the troops marching, indicated by the green arrow, which will fill up as the unit approaches its goal. Right clicking on an enemy held province will launch an attack, indicated with a red arrow.