Collect the quantities relevant to the expression you're looking to calculate. For example, if you're looking to calculate the energy used per person in the United States, find numbers like the census bureau's calculation that the U.S. population in 2002 was 288,600,000 people and the U.S. Energy Information Administration's value for energy consumed in the U.S. in 2002 was 92 quadrillion BTUs.
Round the values to order-of-magnitude ranges, which is the closest power of ten. The population from the example is closest to 100,000,000, so it rounds to 10^8, while the energy number is closest to 100 x 10^15, or 10^17.
Perform the calculation with the order-of-magnitude numbers. For example, energy per person is calculated as the total energy divided by the total number of people. The equation becomes 10^17/10^8 = 10^9 BTUs per person, per year. To convert to kWh, multiply the BTUs by .000293, but in keeping with the other approximations, you can multiply the answer in BTUs by 10^-4. Therefore, the average energy use per person in the U.S. is about 10^5, or 100000 kWh per year.
Evaluate the number for reasonableness. Remember, an order-of-magnitude answer gives you a very rough idea of the size of a quantity; therefore, is it reasonable that the estimate is closer to the real answer than a number ten times bigger or ten times smaller? The example problem leads to an answer of about 10000 kWh per person each month. It's probably a little high, but even so, it's probably closer than 1000 kWh per person per month when you count in the energy to bring your groceries to the store, cool the movie theater or transmit the television signals you use. One way or another, it's not too far off.