Helium balloons work using exactly the same law of buoyancy as water flotation.
As long as the helium plus the balloon is lighter than the air it displaces, the balloon will float in the air. It turns out that helium is a lot lighter than air. Helium weighs 0.1785 grams per liter. Therefore, if you were to fill a one liter soda bottle full of helium, the bottle would weigh about 1 gram less than the same bottle filled with air. That doesn't sound like much - since the bottle weighs more than a gram the bottle will not float.