Small submarines are often called pocket submarines and although the real life ones won't actually fit in your pockets, the one in this Instructable will. It will fit into your pocket and in the water it really does dive and resurface, thanks to different methods of depth control (see step 6 for a movie and step 7 for an additional method).
Above that, it is easy to build from a few components. Apart from the soldering in step 2, which you can do in preparation, you can easily make it in a childrens' workshop. The total cost of materials can be limited to about 6 euros.
This submarine is so simple because of the use of a laminated/moulded solar module, waterproof by itself and by skipping any attempts to waterproof the connections or the motor. Don't worry, many simple electric motors do withstand running them immersed in water. Some of them might corrode somewhat after use, making starting up the next time a little difficult, but For several this will not even be a problem (for hints on which ones see the next step).
"What about the current leaking through the water?" you might ask. This will indeed give a slight energy loss, but it is very limited and the energy comes for free from your solar cells anyway.
I added a short video on March 27th (long video still in step 6):