These last several months I have been considering a lap steel build. I have finally decided to start, and have acquired the pieces of wood for the job (mahogany---8.75"x1.75"x36"---$30). I also placed a stew-mac order that should arive sometime next week. I want to especially thank RomanS for his expertise.
This build will not use routers or electrical cutting machines of any kind. I am cutting, sanding, and shaving with hand saws, rasps, and sanding blocks. There are several reasons to this. One is that I do not have a router (the tool that would make the job the easiest), and do not plan on purchasing one.
Another big reason is to show everybody that it doesn't take a shopfull of tools to build an instrument. If a 16-year old with very little woodworking experience could build an instrument in his spare time during summer break, any of you out there can. In fact, I'm working in the driveway, with everything clamped onto a small table I found in my house!
Unlike some other lap steels, I wanted mine to be a 1-piece body. This requires more curved cutting, etc. Although it may be more challenging, I'm looking forward to it. You can tell by the picture that I haven't picked a headstock shape yet, I'll get to that.
Tools of the trade:

-Stanley Handsaw
-really scary lookin' fat saw
-angle
I've found the best method is to start the cut with fat saw, and to continue it with handsaw. if the cut is started straight (not angled side to side), then it tends to stay that way. I'm really trying to aviod angled cuts, I promise!

However, I started to get careless. I'm worried about these cuts more (where the cut goes deeper into the wood near the bottom) because I'm cutting about 1cm off the pattern. If I angle it too much that way, it may cut into where I want the body.
Here's the grain of the wood. Sorry about the flash, but the one without flash was blurry. I'll try to get another picture later.