As Mike said, you appear to have already extruded once as the tiny faces along the edges indicate that an extrude has occured. Why you are not getting the extrude manipulator is the issue.

I would recommend you try this just to see if you have inadvertantly turned on/off something in your preferences.

1. Open Maya

2. Create a single Poly plane

3. select a single face and then edit poly>extrude face and see if you get the manipulator.

If you do then you have something in your other scene that is wanking you.

You might try deleting the faces including the tiny zero area ones already in your scene (from the screen image you provided). Then use polygon>append poly to recreate the deleted faces, then try to extrude again.

Or maybe export the model then open a new scene import the model will sometimes clear up goofy settings.

As a newbie myself I found out very quickly you have to be VERY careful about accidentally pressing any keys on you keyboard as Maya maps them to all sorts of shortcuts and it is pretty easy to get yourself all wrapped around the axle turing on/off some goofy mode or feature by accidentally hitting some hotkey. Mys favorite way to get screwed up is to select a part and start typing in a name for it and the next thing I know I have hit 15 hotkeys before I realize I did not have the name selected in the channel box!

Worst case the point you are in that model it might be easier to start from scratch.

Good luck,
RAM