When a feather or a plastic bag or almost anything light is placed in water, these items will generally float.  This is easy to understand if you think of water being more dense than the other item.  If you put something heavier in water, it tends to sink like a rock or a piece of metal but this doesn't fully explain how an iron ship can float.

All of these effects are accounted for due to a property all materials have known as buoyancy.  Whatever item has more buoyancy is the item that will float in the other.  This applies also to gaseous systems such as balloons in air or dense gases sinking to the bottom of a room or enclosure.

To understand buoyancy requires understanding density.  Density is the mass of an item divided by its volume.  The mass can be found by weighing the item on a calibrated scale.  The volume of a solid item can be found by submerging the item in water held in a container with vertical walls and looking at the change in water height after the item is submerged.  The volume of the item once submerged in a container of water like this is then found by multiplying the area of the surface of the water by the change in height after the item was submerged.

As an example, a cylindrical jar could be filled around half way full of a liquid with the liquid height marked.  If the item whose volume is to be measured (such as a can opener or a pair of scissors) were placed in the liquid so as to fully cover the item, the increase in volume of the liquid in the vessel would equal the items volume.

If the item is a liquid, its volume can be measured in a graduated cylinder.  If the item is a gas, then its volume at a given temperature would have to be measured in an air tight container.  The mass of a liquid can be found from the weight of the liquid in a container after subtracting the containers weight from the total (which would normally be found by weighing the container prior to placing the liquid in it).

The mass of a gas requires a bit more but can usually be reasonably approximated by the ideal gas law which is an algebraic equation relating pressure, volume and temperature (if the molecular formula for the gas is known such as whether it is natural hydrogen, oxygen or nitrogen gas etc.).

Knowing the mass and volume of a material, its density is then just the value calculated from taking its mass and dividing this by the materials volume.  If the mass is given in grams or pounds and the volume is given in ml or cubic feet, then the density would be given in units of grams per ml or pounds per cubic foot respectively.

To determine if one item will float in a given substance, you need only know that items density and the density of the substance you will be placing it in.  In the case of an iron ship, the total weight of the water pushed out of the way by the ships bottom must have an equal weight of the total ship to cause it to float.  This of course only occurs by having a hollow ship.  The average density of the ship has to be sufficiently less than that of water so that a large portion of the ship stays above water.

When it comes to something like a helium filled balloon or the much larger hot air balloons, the basic principle is the same.  By heating the air in the balloon, the density of the air substantially reduces (by the ideal gas law) so that the whole balloon on average has a lower density than the air around it.

When it comes to filling a balloon with helium, helium atom has much less mass than that of either oxygen or nitrogen molecules so that helium as a whole is much lighter than air.  To make a rubber balloon float then only requires filling it with enough helium so that its total volume has an average density less than that of the air in which it is placed.  By this principle, an iron ball can float in a pool of liquid mercury and oil floats in water.

The complexities of the skeletal infrastructure might require detailed beryllium supports, beams and bracing but buoyancy could allow one to make a working lead zeppelin (i.e., a large helium filled dirigible balloon made of lead).  Theoretically, it would then be possible to fill a lead zeppelin having a sufficiently thin reinforced skin with enough helium to cause it to float.