Hi eric, yeah that curve won't automatically convert to a plane because it's not flat:






So you won't be able to create a simple plane surface through that non-planar curve, and if you extrude it, it won't get caps on the end because extrusion only knows how to build a cap for a planar opening (unless you extrude a surface in which case it can copy the surface to each side to make the caps).

So one way to solidify this object is to draw in some additional lines like so:




Now you can select 4 sided regions and use the Network command to fill in a surface for each region, so for example select these 4 lines:



Then run Construct > Network to build this surface:



Then go select these 4 lines and run Network again and so on:




It can be easier to build something like this by starting with a big solid extruded block and then doing booleans to carve off some pieces - that way it stays as a solid the whole time.

See this recent post for an example for how to carve off some gently rounded sides off of a block:
http://moi3d.com/forum/index.php?webtag=MOI&msg=4296.5

Also I'll see if I can give you an example on your shape.

- Michael