Convergent boundaries:
Plates (oceanic and continental) move towards each other and collide.
1. Oceanic collides with continental - Oceanic plate tips down and slides beneath the continental plate, forming a deep ocean trench. This is called subduction. When the continental plate lifts up, it also forms mountain ranges. In addtion, the oceanic plates melts and is often spewed out in volcanic eruptions.

2. Continental plates collides - The crust crumbles and buckles into mountain ranges. (India and Asia crashed about 55 million years ago and slowly gave rise to Himalayas.) As the mash-up continues, the mountains get higher.
3. Oceanic plates collides - One of the plates will be subduct below the other, forming deep water trenches. These types of collision may also lead to underwater volcanoes that eventually built up unto island arcs.
Divergent boundaries:
Plates move away from each other.
Magma from deep in the Earth's mantle rises towards the surface and pull apart plates, mountains and volcanoes then rise along the seam. This process renews the ocean floor and widen the giant basins. (A single mid-ocean ridge system connects the world's oceans, making the ridge the longest mountain range in the world.)
On lands, giant troughs (Great Rift Valley in Africa) form where plates are tugged apart. (If the plates continue to diverge, millions of years from now easter Africa will spilt from the continent to form a new landmass.)  
Transform boundaries:
Two plates grind past each other along what are called strike-slip faults. These don't produce mountains or oceans, but the halting motion often triggers large earthquakes, such as the 1906 one that devastated San Francisco.

The upper mantle of earth is formed of magma, which flows very slowly. The temperature difference between the inside and outside causes convection currencies to form. Hot material is expanding and thus lighter and so it ascends, then cool down and shrinks, becoming heavier and going down again. While flowing horizontally below the crust, these flows introduce a force and thus a movement into the plate. This is the force behind all *tectonics in the crust.

Tectonics: the study of the Earth's crusts and the force that change it.
              :to, causing, or resulting from structural deformation of the earth's crust.