I'm involved in FRC, so I can't speak for FTC, but I've seen winning teams that designed their entire robot with 3D CAD, but I've seen other winning teams with robots designed with pencil & graph paper. I personally like CAD because things seem to fit better & require less rework. Plus it's fun!
If you want to learn SolidWorks, here are some online tutorials:
http://www.solidworks.com/sw/resourc...-tutorials.htm
http://www.youtube.com/playlist?list=PL0D787F194B340A78
And you can search Amazon.com for SolidWorks books. The neat thing about Amazon is you can "look inside" most books before you buy them. CAD books are expensive. If that's a problem, you can buy an older title (for example SolidWorks 2010) or a used book.
You also might want to conact the closest SolidWorks User Group:
http://www.swugn.org/. Even if there aren't any local SWUGs, maybe you can find someone in your state that can help via web meeting (Webex, Skype or Join.me).
Good luck!
I know what "finished" means, and I know what "robot" means, but what is this "finished robot" of which you speak? - Rick TYler [more] 
19-10-2012, 17:48
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