It's a bit like enzymes (if you know your chemistry): you fix onto a molecule or two, then twist or pull or push in a precise way until a chemical reaction happens right where you want it. This happens in a vacuum, so you don't have water molecules bumping around. It's a lot more controllable that way.
So, if you want to add an atom to a surface, you start with that atom bound to a molecule called a "tool tip" at the end of a mechanical manipulator. You move the atom to the point where you want it to end up. You move the atom next to the surface, and make sure that it has a weaker bond to the tool tip than to the surface. When you bring them close enough, the bond will transfer. This is ordinary chemistry: an atom moving from one molecule to another when they come close enough to each other, and when the movement is energetically favorable. What's different about mechanochemistry is that the tool tip molecule can be positioned by direct computer control, so you can do this one reaction at a wide variety of sites on the surface. Just a few reactions give you a lot of flexibility in what you make.