Creating polygon primitives: if the "drag the shape on the ground plane" method seems kind of sloppy, turn it off:
Create->Polygon Primitives->Interactive Creation.
Tool / Command Options: most Maya menu commands have this little square next to them. That's the Options - click it instead of the menu item to get extra control over the tool or command. With Polygon Primitives, for example, you can set the number of subdivisions and the size of the object.
Component Editing: R-Click the object and pick the component type you want to manipulate. Then use the Move, Scale, Rotate tools. R-Click the object and select "Object Mode" to go back to editing the whole object.
Soft Selection Sculpting: In Component Mode, use the move tool (w). Open the Tool Options panel. Turn on Soft Selection. Dragging components will stretch and deform the surface.
Extrusion: use this to grow new geometry out of an existing object.
- Select one or more faces
- Edit Mesh->Extrude
- Use the extrusion manipulator to pull the new extruded faces out of the mesh
Split Polygon Tool: use this to cut a polygon into smaller pieces to add detail.
- Edit Mesh->Split Polygon Tool
- Click on one edge of a polygon
- Click on an edge on the opposite side of the polygon
- Press Enter to complete the action
Insert Edge Loop Tool: inserts a whole loop of edges all the way around an object.
- Edit Mesh->Insert Edge Loop Tool
- Click on an edge you want to split, as with Split Polygon. A whole edge loop appears.
Cutting Holes in Things:
- Select a Face
- press Backspace to delete it
- You can also delete edges, to simplify geometry if it's too complex.