The formula governing the parameters describing a gas in normal temperature and pressure ranges is the ideal gas law: PV = nRT. Here, V stands for volume, P for pressure, T for temperature, and n for molecule count. R is a proportionality constant called the "universal gas constant." It makes all of the units fit together. So n/V measures density. The n can be converted to grams to put the measure in everyday terms.

Measure or identify T, P, and V of the gas.
For example, if you pump up a bicycle tube that's 27 inches in diameter with a diameter of 1 1/2 inches, that's a volume of 150 cubic inches. Pump the tire up to 90 PSI, according to the pump's gauge. Assume the temperature hasn't changed and therefore is room temperature: 72 degrees Fahrenheit.

Convert the terms to scientific units in order to use the more commonly known conversion factor in the ideal gas equation.
Seventytwo degrees Fahrenheit translates to 295 K (degrees Kelvin); 150 cubic inches translates to 2.458 L (liters); 90 PSI translates to 6.124 atm (atmospheres).

Calculate the ratio n/V using the ideal gas law: n/V = P/RT, where R = 0.08206 amtL / molK.
Continuing with the above example, n/V = 6.124/0.08206*295 = 0.2530 mol/L, where mol means "moles," a measure of molecule count.

Convert the moles per volume to grams per volume.
The molar mass of air is 28.8 grams per mole. So 0.2530 mol/L converts to 7.29 grams per liter. This is the density of air in a bike tire at 90 PSI, or 6.1 atmospheres. That's the weight of about seven pennies in a tire.
Tips & Warnings
 As discussed in Chang's "Chemistry," the ideal gas law is appropriate up to 150 PSI, or ten times normal atmospheric pressure, when the van der Waals equation starts becoming more appropriate. That's when intermolecular forces and the finite size of the molecules starts playing a significant role.
References
 Photo Credit air pump image by gajatz from Fotolia.com