Float the house on logs. This is the traditional method of constructing a floating house. The logs must have a large diameter even for a small house. Typically, a deck is built on the logs and then the house is built on top of the decking. The disadvantages to using logs are that they are prone to water damage and infestation by pests such as the Teredo worm.
Purchase pre-built floats or a float house base made from materials such as expanded polystyrene foam coated in glass fiber reinforced concrete. Many boat harbors use these types of floats. The advantages are that they are fireproof, bug proof, very durable and virtually unsinkable. They are also rigid and engineered to prevent any torque or sagging. The environmentally inert materials dispense with the use of old growth logs and eliminate many maintenance chores including the use of toxic paints.
Float the house on a barge. If you want a big float house, find a used barge and build the house on the barge deck. This is how the bunkhouses for many logging camps in Southeastern Alaska used to be constructed.
Float the house on one or more boat hulls. Purchase a used boat hull or build your own. The easiest boat hulls to use are pontoon boats with flat party decks or use a catamaran hull. Build your own hull from plywood and fiberglass or weld one from aluminum.