The gas laws are a set of physical laws that govern the behaviour of gases. There are several gas laws, and remembering whether the relationship between any two variables is direct or inverse can get annoying. Luckily any of the gas laws can be derived from the easily remembered ideal gas law.

For this guide the following conventions will be used:
Volume (V): Measured in liters (L), the amount of space the gas is constrained to.
Amount (n): Number of moles of a gas.
Pressure (P): The pressure of the gas in atmospheres (atm).
Temperature (T): The temperature of the gas in Kelvin (K).

Boyle's Law:
The volume of a gas is inversely proportional to pressure when the amount of gas and the temperature are held constant.
V = k / P
Therefore, P1 * V1 = P2 * V2

Charles' Law:
The volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant.
V = k * T
Therefore, V1 * T2 = V2 * T1

The volume of a gas is directly proportional to the amount of the gas present when temperature and pressure are held constant.
V = k * n
Therefore, V1 * n2 = V2 * n1

Using the gas laws:
The basic idea is that in any applicable problem, you will be given three out of the four variables. Usually the problem will say something like "Gas Y occupies 5 L at 50 K. When pressure is held constant, how much volume will the gas occupy at 100 K?" In this case Charles' Law is applicable, as we know V1, T1, and T2, and are asked to find V2. Notice that the other variables dealing with gases must be held constant, otherwise this law cannot be used.

The game gets more difficult when more variables are introduced. Rather than memorize the formulas relating V, T , and n, or those relating P, T, and n, or those relating P, V, and T, and so on, we use a new law, called the Ideal Gas Law.

Ideal Gas Law:
The pressure and volume of a gas are directly proportional to the amount of the gas and the temperature.
P * V = n * R * T
Because all aspects of gases are included in this formula, the constant R is global, and is defined as .082057 Liters * atmospheres per mole * kelvin (.082057 (L*atm)/(n*K) ).

Using the Ideal Gas Law:
The standard use for the Ideal Gas Law would be for application in a problem such as the following: "5 moles of Gas Z is retained within a 50 L tank at a temperature of 100 K. What pressure will exist inside the tank?" In this case we are given n, V, T, and we are asked to find P. We also know the constant R. This is enough information to solve the Ideal Gas Law for pressure.

Deriving the Gas Laws from the Ideal Gas Law:
As mentioned above, there is no need to memorize the individual gas laws, with the exception of the Ideal Gas Law. Let's suppose that we have the aforementioned problem "Gas Y occupies 5 L at 50 K. When pressure is held constant, how much volume will the gas occupy at 100 K?". We know that we need some relationship between volume (V) and temperature (T). To find the applicable law we simply solve the Ideal Gas Law for our two variables:
P * V = n * R * T
(P * V) / T = n * R
V / T = (n * R) / P
We know that n and P will be held constant, and of course we know that R will not change, therefore we can say:
V1 / T1 = (n * R) / P
V2 / T2 = (n * R) / P
And therefore:
V1 / T1 = V2 / T2
Rearranging yields:
V1 * T2 = V2 / T1
Which happens to be Charles' Law! Now we just need to plug in the values we were given and solve.

More Complex Derivations of Gas Laws:
"2 moles of Gas Q occupies 50 L at temperature 100 K. When pressure is held constant, how much volume will 3 moles of Gas Q occupy at 500 K?"
In this problem we need a relationship between volume, temperature, and amount. There is no specific gas law for this, but we now know that we can solve the Ideal Gas Law for whatever variables we need. So let's do it!
P * V = n * R * T
(P * V) / T = n * R
V / T = (n * R) / P
V / (n * T) = R / P
In this case, we know that R and P will be constant, so:
V1 / (n1 * T1) = R / P
V2 / (n2 * T2) = R / P
And therefore:
V1 / (n1 * T1) = V2 / (n2 * T2)
Rearranging gives:
V1 * n2 * T2 = V2 * n1 * T1
Now plug in our values and we're done!

Conclusion:
It is important to note that this node deals with ideal gases only. If a gas is not perfect, it will deviate from these laws. No gas is perfect, but in most situation the Ideal Gas Law and its variations are accurate enough. For situations in which accuracy is of extreme importance, various real gas laws may be used.

With any luck you can now use the many forms and properties of the gas laws without too much memorization.

Related subjects:
Ideal Gas Law
Real Gas Law