The answer is sort of in the question... air, which is 78% nitrogen and 21% oxygen. Normal air is most commonly used to fill cylinders because it is the cheapest gas to fill cylinders with.
Although air is what most diving cylinders have inside them, some people do something called nitrox diving. This is where the air is enriched with pure oxygen. This increases the time a diver can stay at any depth without needing to decompress. Adding pure oxygen means that special equipment is required to fill the cylinders and also breathe it because it needs to be 'oxygen clean'.
For very deep diving the mixtures change to tri-mix which is a blend of nitrox and helium or heliox which is just helium and oxygen. These mixtures are used because nitrogen causes intoxication at depth. By reducing the amount of it and replacing it with helium these effects are reduced or eliminated. Helium is a rare and expensive gas so these mixtures would only be used when they are required.
SCUBA tanks are metal (usually steel or aluminum) that are filled with compressed air. This is loosely related to a pneumatic system.
Fluid logic.
You could buy your own portable diving compressor, my dive buddy has one, there not silly expensive . You must get fills from a compressor designed for diving (breathing) as the air is filtered and moisture removed.
Because the air is compressed so that the same amount of air fills much less space meaning more can be put into a SCUBA cylinder. Normally a tank will be pressurised up to around 3000psi/200bar of pressure.
Tanks are used to hold air like you breath above water. They do go thru a filtering process that removes the water and other things in air that can harm a diver. Scuba air from a reputable source is very clean and dry.
Most scuba tanks are filled with simple purified air. However, some are filled with oxygen enriched air called 'nitrox' or (less commonly) a blend of helium, oxygen and nitrogen called 'trimix' or (even less commonly) helitrox or heliox.
Hide behind those water tanks. The scuba tanks are filled and ready to go.
so they can breath underwater
The average aluminum SCUBA cylinder holds 80 cubic feet of air at pressure. That means you are taking the equivalent of a closet's worth of air and smashing it into a cylinder much smaller than that. When full, the cylinder is at 3,000 pounds per square inch of pressure.When the valve is opened, it sends air into the (assumed) first stage regulator which is connected by hoses to gear such as two second stage regulators, instruments and your vest.So the SCUBA tanks don't so much USE the air so much as STORE the air at high pressures.
Depents on what depth your at and your personal breathe rate, typical 30-60 Mins at 25 meters,
Under 25
They either go to a dive shop or have their own compressors. An average 80 ci tank costs roughly $5usd to fill