I came across lovely plans for building such a boat from a drink can and a milk carton from Science Toy Maker. The explanation and videos are really clear and easy to follow and the boat worked first time. Here's a short video showing it under test in my sink:
The first step in the instructions is making the engine. It uses a drink can, two straws and some epoxy glue. If you follow the video instructions it's not hard to make. Here's the can with the lid cut off using scissors:
The boat itself uses a milk or juice carton. Here's one I borrowed from someone's party:
The boat is powered by a tea light.