For more information on this "steam" engine that runs on vacuum cleaner power, visit the main steam engine page.
Note that this model is constructed with old school Lego Technic. You can probably use ideas of this design to build your own engine with the newer generation of Lego Technic parts.
Here's a picture of the final engine:
We start with building one cylinder and its piston. For the (upside-down) top of the cylinder we require
Close the two outer holes of the 2 x 4 plate with the round 1 x 1 plates. As such, no air will escape here when pressure is applied to the piston.
Now we add layers to create a box of blocks representing the cylinder. In the bottom and top layer, we leave an open hole, for air (steam) to go in and out of the cylinder.
While building the cylinder, we also build the piston. The piston is an axle, with a 2 x 2 plate attached to it with a bush. I have used the (newer) black bushes, which hold a bit tighter than the grey ones.
And we continue adding layers ...
The technic bricks will serve as the cylinder's pivoting points.
More layers ...
Make sure that the piston can easily move up and down the cylinder.
Finally, we close the cylinder with a lid.
We can now start with some of the framework for the engine
The framework also supports the crankshaft of the engine.
Connect the next brick to the other side of the cylinder with a pin.
The plate and brick in the following step almost finalizes the air inlet of the engine (we need to top it off, which happens near the end). With your model, you can see how the cylinder's inlets align with (two half) holes in the long Technic brick, as it rocks up and down while rotating the crankshaft.
We're halfway through. Now, we create a second cylinder, in similarity with the first. This cylinder is a mirrored version of the first. Make sure to put the inlets of the cylinder on the mirrored side.
Finish up the crankshaft.
Now, we finish the framework.
And we close the engine's air inlet
More strengthening of the framework.
Finally, we add a flywheel to the axle of the engine. Just use the biggest wheels you have.
You are now ready to roll out your engine. To run the engine, grab the nearest vacuum cleaner, turn it on, and suck air through the machine by holding the vacuum cleaner's inlet to the air inlet of the engine.