To see that ice takes up more room than water does, stick a piece of tape to a glass of water. Fill the glass with water up to the tape, and put it in the freezer. When the water is frozen into ice, take it out. Is the water at the same level it was at before?
It's a good thing for us that ice floats, because otherwise when the top of the oceans froze, that ice would sink to the bottom, and then the new water on top would freeze and sink to the bottom, and pretty soon the oceans would be frozen solid and we would have no water to live on.
Bibliography and further reading about ice: