They are not the most useful ones I know of (selection tools [A, B, B - B, right Mouse Button, shift + right Mouse Button], extrude [E], and delete [X], grab [G], scale [S] rotate [R]), but for subdivision surfaces they are very necessary.  I will demonstrate them in a common subdivision surface situation.  For simplicity, I will be starting with only one quadratic face.  Although drawn in wire frame throughout, it is always completely filled in when rendered. 

I assume you know how to do basic mesh editing.  

	This is the quad we will start with.  Select the left two vertices.
	Here it is shown with the left two vertices selected.  Subdivide this edge.  To do this press the 'W' key to open the specials menu.  Choose subdivide.  What subdividing will do is easier to see than explain.
	This is the result of the subdivision.  It added another vertex between the selected two, along the selected edge, and changed the quad face we started with into 3 triangles.
	Select only the top two vertices, and subdivide their edge.
	Result
	now select the vertices indicated in yellow.
	Press Control + 'F' to swap their shared edge.  The result will be the picture on the left.  This is one of the useful functions here...
NOTE: if you had subdivided the top and left edge at the same time you would not of had to switch any edges, but many blender users don't think that far ahead, and don't know it is possible, or if they do know they don't know how.
	select the same vertices as I have here.
	Subdivide them as I have.
	select these vertices.  NOTE: I moved one of them a little.  It may be a good idea to do the same.
	Press Alt + 'J' to join them into a quad.  This seems to work with multiple vertices as well, but I find it less predictable which ones it will decide to join.  The result is on the left.
	same idea as the last to steps, but combined into one.  Select the vertices in yellow, and join them into a quad.
	same as above.
	Completed, after deselecting all vertices.

As this is best for subdivision surface modeling I should probably include some links to the basic ideas of it.  At the moment I can not, but I hope to in the future.  Don't expect miracles.  

One more thing: Control + 'T' will convert to triangles.  ... But subdivision surfaces (my current technique-in-progress) doesn't need triangles (usually).