Before anything, make sure that the object is properly orientated. If the object displayed is like that because it's rotated in object mode, you should be able to get it out pretty easily. If not, I suggest you read this. You want the top flat surface to be perpendicular to the Z axis.
As for how I would go about this, with my 2D object (seen below):
Select the bottom edges that you want to extrude.
Press E to extrude them and press Z to lock that extrusion to the Z axis. Feel free to extrude them however much you wish, just make sure that everything is extruded down so that all the highest of the selected vertices (the ones you are moving down) is below the lowest of all the other vertices. Otherwise, you'd have those coming out the bottom of your object.
Press S to scale the selected edges, Z to limit scaling to the Z axis, and 0 to scale to 0.
From this point, it's just a matter of going around, selecting the open edges of your mesh and filling them in.
I hope this helps and if you have trouble, let me know in the comments.