Ultimately, two things cause the Earth's surface to look the way it does: Plate tectonics and erosion (life is also important but its exact effect on geology and the surface appearance is complicated, not well understood, and not discussed here).
I. Plate Tectonics - the theory that the Earth's surface can be described as a set of rigid plates moving about the surface relative to each other.
A. Mathematics of plate movements:
1. Each plate can be described as moving horizontally along a great circle and/or rotating about a fixed pole through the Earth's center. The former is called "poloidal" motion and the latter is called "toroidal" motion (great circle - a circle drawn on a sphere whose radius is that of the sphere).
2. There are only three possible types of plate boundaries:
a. Convergent boundary- one plate is subducted into the interior as the other plate overrides it.
b. Spreading center - two plates are moving apart from each other, and new material must be produced at the boundary to fill in the gap.
c. Transform fault - two plates are sliding past each other.
3. At most three plates can meet at any single point in a stable configuration, these points are called "triple junctions." Note that plates, plate boundaries, and triple junctions all move about the surface relative to any fixed reference frame.
4. Some interesting details:
a. transform faults and spreading centers fall along great circles.
b. subduction zones (convergent boundary) trace a small circle on the Earth's surface, giving an arc appearance from above. To first order the curvature of the arc is indicative of subduction dip angle, with shallower dip angles having a smaller radius of curvature (to visualize this imagine slicing a chunk of material off of a sphere. The outline of the cut is a small circle).
c. theoretically, in order for two plates to move apart on a sphere the spreading velocity must change continuously along the spreading center. In reality, the plates are lots of mini-plates separated by transform faults, where each mini-plate has a single spreading velocity. The end result is that spreading centers are segmented.
d. Hotspots (intraplate volcanoes: Hawaii, Bermuda, etc.) appear to remain fixed relative to each other and Earth's rotational pole; thus, they provide a fixed reference fame for calculating absolute plate motions. As plates pass over hotspots they leave tracks of volcanoes (e.g., the Hawaiian - Emperor chain). Why they are fixed is a largely unanswered question.
e. A convecting single-viscosity fluid has no toroidal motion; that such motion exists requires lateral viscosity variations in the mantle.
f. Neither plate convergence nor plate spreading are required to occur perpendicular to the plate boundary. That it does generally happen that way is thought to be related to minimizing energy expenditure.
B. The appearance of plate boundaries
1. Transform faults
a. Pre-fault features cut by the fault are offset from each other. If looking from one side of the fault to the other, movement is described as "right-lateral" or "left-lateral."
b. If fault trace gets covered with sediment can end up with unrelated geologic features right next to each other for no apparent reason.
c. Dragging along the boundary can form s-shaped folds and fractures.
2. Spreading Ridges
a. Typical section of oceanic crust with depth
sedimentary rock 0.5 km
pillow basalts 1.7 km
basalt/diabase dikes 1.8 km
gabbro 3.0 km
peridotite
undepleted mantleb. Cooling of lithosphere away from ridge makes water depth proportional to t1/2 or d1/2.
c. Continental rifts.
i. Usually sinuous in planform.
ii. Faulting usually asymmetric.
iii. Can develop into ocean basins bounded by "passive margins" - an ocean continent boundary that is not a plate boundary.
3. Subduction Zones
a. Bending of downgoing plate creates "flexural bulge" ahead of trench. Shape and height of bulge can be used to estimate the thickness of the elastic lithosphere.
b. A topographic trench forms between the downgoing and overriding plate
c. Downgoing plate brings water into mantle, lowering the melting point of rocks in the overriding plate. Volcanic arc usually occurs ~100 km from trench. These volcanics are usually dominated by andesites and granites, and the process may be an important way to form continental crust.
d. Depending on the force the downgoing plate exerts on the overriding plate, the overriding plate may spread (back-arc spreading, e.g., Sea of Japan) or contract (mountains, e.g., the Andes).
e. Continental crust never subducts; continent-continent collisions produce huge mountain ranges.
II. Erosion.
A. Types
1. Water - glaciers, rain, rivers, oceans, etc.
2. Wind - minor but significant
3. Chemical - by itself, fairly insignificant
B. Effects, especially from an orbital view
1. Sea level is an erosional base level, resulting in a bimodal distribution of topography: one mode is the ocean floors for oceanic crust, and near seal level is the mode for continental crust.
2. Erosion quickly buries or removes the surface expression of all but the largest faults. Thus, for a typical tectonic setting it is easier to understand the big picture but difficult to fill in the details.
3. The original topographic shapes of tectonic features are usually cut and distorted by water erosion. Comparisons of these features to those on other planets is difficult.
4. Sedimentation makes old and highly deformed crust, like the continents appear flat and buries craters very effectively.
III. The Interior
A. Chemical layers of the Earth
1. Crust - ~0.5% of Earth's mass. Two types, oceanic and continental:
a. Oceanic - density ~2900 kg m-3, ~7 km thick, mostly mafic rocks. Oceanic crust + cool mantle lithosphere is more dense than underlying mantle.
b. Continental crust - density 2000-2800 kg m-3, 20-80 km thick, lots of felsic rocks. Continental crust + cool mantle lithosphere is less dense than underlying mantle. Continental lithosphere sets higher topographically than oceanic lithosphere because of isostasy (the same mass of material at a lower density makes a taller column that "floats" on the mantle below).
2. Mantle - base of crust to ~2900 km depth. 2/3 mass of the planet. Density increases from 3200 kg m-3 below the crust to 6000 kg m-3 at its base. Components - mostly olivine, some orthopyroxene, and a little clinopyroxene and garnet. Significant seismic discontinuity at 670 km is either a phase change boundary of a compositional boundary (probably the first).
3. Core - 1/3 mass of the planet. 2900-5200 km depth is liquid Outer Core; 5200-6371 km is solid Inner Core. Composition is mostly Fe-Ni, with an unknown light element.
B. Mechanical layers:
1. Lithosphere
a. thermal - ~100 km in old oceanic lithosphere, and 100-200 km under continents.
b. elastic ~20-30 km in old oceanic lithosphere and continents.
2. Asthenosphere - low viscosity layer below the thermal lithosphere, ~100-200 km thick. The presence of this layer, acting as a lubricant, may be necessary in order for the lithosphere to behave as large, rigid plates.