Common Modeling tools and operations

Below are some of the more common menu commands used when modeling in Maya.

Deformers:
Create Deformers> Create Lattice
Create Deformers> Non-linear > Bend, Squash, Twist, etc

Mesh:
Edit Mesh > Keep faces together (turn on/off to change the way extrude works)
Edit mesh> Extrude (push/pull/scale in/out a selected face)
Edit mesh> Split Poly tool
Edit mesh> Cut Poly tool (use sparingly - can make geometry messy)
Edit mesh> Merge (welds vertexes together)
Mesh> Combine (combines multiple polyObjects into one)
Mesh>Sculpt Geometry Tool
Mesh> Booleans

Surfaces:
Revolve
Loft
Extrude

Misc
Edit> Delete By Type> History - deletes "history and bakes in shape changes
Modify>Center Pivot (moves object's pivot to its center)
"G" hotkey - repeat last command (Ex: Extrude)
"Y" hotkey - repeat use of last tool (Ex: Sculpt Geometry Tool)