Just starting out, created a planar mesh, in edit mode, hit E to extrude, and I get this:
Extrude doesn't create any perpendicular faces or vertices, it just duplicates the flat mesh and grabs it. What's going on here?
I think you might have hit Extrude once, and not moved the mouse and now there are duplicates of every vertex. You can remove doubles and Extrude again, should work fine.
This is what you're seeing:
Select everything, press W -> Remove doubles. Then try to extrude again:
This is what you want to see