how do boats float

They're not heavy enough to push the water out of the way to make room for them to sink.

by displacing an amount of water which is equal to its own weight.

Buoyancy is the upward force on an object produced by the surrounding liquid or gas in which it is fully or partially immersed, due to the pressure difference of the fluid between the top & bottom of the object. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body. This force enables the object to float.
If u add too much weight, people or cargo, the boat will displace more water, freeboard will decease to zero (0) & the vessel will now sink.
An object, or boat, can displace water & still sink. A boat can have poor stability & still float, at least in calm waters.

''surface tension'' is the phenomenon of water molecules sticking together, like when two drops of water on a desktop combine to form one bigger drop of water. It is what keeps a boat from falling between the water molecules the way it falls through air molecules.

The boat pushes down on the surface of the water with a force equal to the weight of the boat. The surface of the water pushes up on the boat with a force equal to the weight of the water that is displaced (the volume of water pushed out of the way by the boat).

The boat sinks until it has displaced a volume of water that weighs the same as the boat, & floats at that depth.

How does a heavy boat float?

A boat, or any other object designed to float, is based on a theory by a very old guy, even older than Capt. Matt. Though he is old and, by the way, dead, he was really a cool guy & his name was Archimedes (Ark-i'-meed-eez). His principle, cleverly named the Archimedes' Principle, explains how things float.
If u fill ur bathtub with water, what happens when u get in? The water rises, right? (And sometimes goes over the side.) That is because u ''displaced'' some of the water with ur body & it had to go somewhere. The key to floating is that the object must displace an amount of water which is equal to its own weight.

For example, suppose u had a block of wood that was 1 foot square. Let is say that this block of wood weighs about 50 pounds. Now say we lower that wood into the water. The wood will move down into the water until it has displaced 50 pounds of water. That means that fifty pounds of water r pushing back up on the block & making it float.

The principle of floating is pretty easy, however, if u want to remain inside the boat & actually get where u want to go, ur boat must have ''stability'' as well as being able to float. Stability means that it is designed not to tip over easily. That does not mean it wo not ever tip over.