You will need:
A Model Kit (mine was an Airfix 1:72 scale Spitfire mk1a)
A micro-motor (I got mine from an old r/c boat; also available from the internet, including here: http://www.wheelspinmodels.co.uk/i/93255/)
DPDT Switches x2
Quality cardboard (about 2mm thick)
Craft knife (I used a small pocket knife)
Soldering iron + solder
In all, mine cost me £7 (about $10, I think), £5 for the kit and £2 for the paint. I had all the tools and glues already. If you were buying the motor, this would add another £4 to the cost. It's a cheap and cheerful project, this one!
Step 1: Pre-painting the kit.
Paint all small, non body-coloured parts (such as the prop, wheels and exhausts) while they are still attached to the plastic frame. These parts are glued on later, after the body has been painted and this reduces paint bleed and overlap.
Follow the instructions for the kit until you get to putting the fuselage together. This is when we add the Motor (and lights if you have the space).