Step 1: Step 1
In my case, a dumpster appeared while campus was remodeling a building - goodies ahoy.
Look for some wood that's atleast 1.75" by 20" ... bigger would be better. Hard wood is best... i think my is pine
Step 2: Step 2
Cut it to the rough length you need for the neck - I made my neck 19", and I made the head from a second piece (I suggest against this, but it's your call). I also made the portion that attaches the neck to the body separate... again, I suggest making it one piece (mine kind of bows there).
Step 3: Step 3
A saw helps with this part. Power tools really help here... I didn't have much for power tools.
So, i penciled a vague banjo shape, and sliced off the parts that didn't look banjo-y to me. There was lot's of whittling with my pocket knife to get the final shape. Try using a bandsaw if you can.
Step 4: Step 4 (optional)
I highly advise against this step, but if you want to follow my example, more power to you.
It looked pretty bad until i washed the blood off.
Step 5: Step 5
This means more bandsaw/coping saw/pocket knife work.
Step 6: Step 6
Make the shape comfy - round off the corners, blend the different sections together, etc.
On mine, the Neck was 19" from the Nut (the top part by the tuners) to the cookie-tin, and the 5th string's last fret was 663 mm from the Nut (with the tuner peg a bit above that).
At the nut, mine was about 1 1/2" wide, and at the base, it was about 1 7/8" wide.
1/2" to 3/4" thick is plenty good... do what ever looks good to you.