How can I trace an image to create an object? For reference material, I've loaded an image onto a plane and made it un-selectable. Now I'd like to "trace" it by clicking to create a series of vertices, make them into a path, turn that path into a plane, then extrude the plane into a 3D shape. (In Photoshop terms, I'd like to use the Blender equivalent of the Polygonal Lasso tool to create and fill a selection with color.)

So far, I've been doing this by adding a plane, then subdividing and pushing around individual vertices until I have enough to approximate my reference. It's a slow process and it strikes me that there's likely a better approach.
You can hit e to extrude a vertex or you can ctrl + right click to extrude to mouse position. F while two vertices are selected will join them with an edge, and if you have an edge loop selected the same f will fill it with a face.