Hello Frances,

Select your curve and go into the Object menu (at bottom, leftish) and go up to Convert to make your curve into a mesh object. Once it's a mesh, go into Edge mode* (once you're in Edit mode by pressing tab) and select it. You should be able to extrude to your heart's content.

Something to remember...when you extrude a point, it becomes an edge. When you extrude an edge, it becomes a plane (face).

Hope this helps!

James

* - there are three major editing "modes"...working with Vertices, working with Edges, and working with Faces. In more complex modeling, you will find the need to switch among the three depending on just what you're doing at the moment. (more on that later)