Making up the thin wood panels for the top & back (and sides) is not as difficult as it may seem. You need to be able to re-saw, but as small as a ukulele is this can be accomplished on most any table saw.
Clean up the edges so they fit tightly together, and on one side, tape them with masking tape:
Flip the whole thing over, bend the joint open and glue, flatten it out, wipe off the excess glue, and weight it down to dry:
When the glue is throughly dry, remove the tape and sand the panel smooth with a belt sander. With practice, you can get very even thickness this way - just flip the panel end for end and over frequently, and check your progress often. Note the wood stop piece tacked to the edge of the work bench.
Finish by hand with a sanding block. You are after about 3/32" thickness.
Next: Assembling the neck & sides
If you find any of this helpful I'd certainly appreciate a "tip" :-)