Here's a very easy to make steam engine, Hero's steam engine. It's named after Hero of Alexandria who described it in a document in the 1st century AD.
It consists of an unopened soda can with two tiny holes in either side and a little water inside. Heating the can heats some of the water to steam, which escapes out the holes in the sides. The holes are made such that the steam comes out at an angle that propels the can in circles.
How to make this Hero's steam engine
Step 1. Use a pin to make a hole in the side of a soda can. The can must still be unopened. When you pull the pin out there will likely be some spray.
Step 2. Empty the can through the pinhole. Depending on the soda in the can, shaking it will increase the pressure in the can causing the soda to come out faster. Don't worry if there's a little soda left when you're done.
Step 3. Make another hole in the other side of the can.
Step 4 Put the pin back in one of the holes and pull it down as shown in the photos below. This modifies the hole enough for the steam to later come out at an angle with respect to the can.
Step 5. Do the same for the other hole, pulling the pin in the same direction with respect to the can.
Step 6. Put a little water in the can through one of the small holes. It doesn't need to be much, and less is better than more since it takes time to heat the water to steam.
Step 7. To hang the can, find something to hang it from. I hung mine from the arm of a desk lamp. First put a tie strap, then hang a fishing swivel from that, followed by a loop of string. The swivel is the key part here since it has a built in bearing that turns easily. If yours doesn't turn easily then spray it with some WD-40 or other lubricant.
Step 8. Gently lift up on the tab in the top of the can and put the string under it. Make sure you don't break the seal at the top of the can. The only openings in the can should be the two holes you made in the sides.
Step 9. In the photo for step 9 below you can see that there's a small circle (really a rivet) in the top of the can. That circle is in the center, so the string should be centered over that.
Step 10. Light up a propane torch. I tried a lamp that burned rubbing alcohol but it wasn't hot enough. From that I'm guessing that a candle also won't work. The butane flame from a desk torch in a typical physic or science classroom should work. Take all necessary safety precautions.
Step 11. Heat the bottom of the can. Heating it as shown in the photo below takes around 30 seconds for the can to start rotating. When it does, it rotates quite fast.
Here's my video showing it in action along with how to make it.