When you put an object in a fluid, the weight of the object pushes down and the fluid pushes up.

The upward push of the fluid is equal to the weight of the fluid it displaces. It displaces its own volume of the fluid. This is the Archimedes Principle.- - see Archimedes

If the weight of
the fluid a body displaces occupies a volume that is less than that
of the object, the object will float. The buoyant force will equal the
weight of the object in air and the two will cancel each other out.

Will it float or sink?

Whether a body
will float in a particular fluid, both weight and volume must be considered.
We need to look at the density of the body compared to the density of
the fluid.

If the body is less
dense than the fluid, it will float. If the body is denser than the
fluid, it will sink.

If it floats how much will be under the surface?

Relative density
(comparing the two densities) also determines the proportion of a floating
body that will be submerged in a fluid. If the body is two thirds as
dense as the fluid, then two thirds of its volume will be submerged,
displacing in the process a volume of fluid whose weight is equal to
the entire weight of the body.

Apparent weight of a body in a fluid

In the case of
a submerged body, the apparent weight of the body is equal to its weight
in air less the weight of an equal volume of fluid.

Shape and position when floating

In calculating
the buoyant force on a body, however, one must also take into account
the shape and position of the body. A steel rowboat placed on end into
the water will sink because the density of steel is much greater than
that of water. However, in its normal, keel-down position, the effective
volume of the boat includes all the air inside it, so that its average
density is then less than that of water, and as a result it will float.

Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.