If you aren't familiar with how Stirling engines work, there are plenty of resources online- the Wikipedia page is a good place to start.
Step 1: Design
I found that an aluminium drinks can would fit neatly inside a steel soup can, so decided to use that for the displacer on the grounds of being cheap, light and easy to work with. The steel soup can provides a sturdy body for the engine and also meant I could ake the bottom removable to allow maintenance.
I found some decking to use as the base, some 1" x 1/2" pine to use as supports for the moving parts, and a piece of 3/4" aluminium strip to use as the beam. The engine is a messy combination of metric and imperial units- that's what happens when you use scrap materials!