Why Boats Float
Boats float because of the principle of displacement. Gravity is constantly pulling down on everything, even objects placed in the water. At the same time gravity is pulling down on your boat in the water, the boat is also pushing water aside. If gravity pulls stronger at the boat--in other words, if the boat weighs more--than the water it pushes aside, the boat will sink. But if the boat weighs less than the water it pushes aside, it will float.
Why Styrofoam Floats
While the principle of displacement lets even heavy materials like steel float, if shaped and distributed properly, a chunk of Styrofoam will float no matter how big or small and no matter the shape. Styrofoam has very low density; it weighs very little compared with the amount of space it takes up.
Styrofoam is cheap and readily available, which makes it perfect for building a toy or craft boat. Even though it floats well, Styrofoam wouldn't make a good boat for long-term use by people because it is so fragile.
Boat Building Material
The best Styrofoam toy boats are made from one solid piece. You might try using pre-formed Styrofoam packing if you have any from a large appliance such as a television or microwave, or you can purchase blocks of Styrofoam from your local craft store or perhaps a florist shop. Use closed-cell Styrofoam. Open-cell foam, which has a honeycomb-like structure, absorbs water, becomes heavier and eventually sinks.
Making the Boat
Use a utility knife to carve a rough boat shape out of the Styrofoam block, then go back over the shape and smooth it out again. You may need to replace the blade in your utility knife once or twice in the course of this carving process; the sharper it is, the better and easier it will work. Paint the boat with latex craft paints.
Stick a thin wooden dowel straight into the Styrofoam for the mast. Pull the mast back out, put a bead of glue in the hole to help keep the mast from turning, then put the mast back in the hole. Tie or glue a pair of dowels perpendicular to this mast, one near the top and the other about halfway down, then tie a handkerchief onto this rigging by looping thread around the corners of the kerchief and then the ends of the sticks. As soon as the glue on your mast and the paint on your boat have dried, you're ready to put it in the water. Don't forget to tie a long string--kite string works well--to your boat so you can pull it back if it sails too far away.