Maya - Modeling Basics

Vertex - A singular point on a 3D model, by which two or more edges connect to.

Edge - A line connecting two vertices together in a 3D model.

Face - The flat plane created by the intersection of connected edges and vertices.
This is often a square or rectangle shape, but can be other shapes as well.

Extrude [Ctrl + E] - Take selected face(s) and extend them inward/outward. Extremely useful tool, and one of the most commonly used.
This is effectively your bread and butter for most forms of modeling.

Combine - Takes two or more separate objects, and combines them into a single object. This DOES NOT mean the objects are necessarily connected. But this is required in order to connect them.

Bridge - Takes two selected edges and creates a new face to connect them together.

Bevel [Ctrl + B] - Add additional edges to selected face, to create a rounded look.
Note: If going for "clean" topology, depending on what you select, this might create non-quad faces.