Introduction:
Every serious growing box needs cooling. Most of us use air cooling because it is cheap and very effective. The following steps are used to design a simple fan-cooled box.
This method does not cover active cooling with air conditioning systems or 'CoolTube' designs. It is for grow chambers where the walls are approximately equal to the light pattern, totally enclosed for airflow control, and do not have large radiant heat into or out of the box. Your mileage may vary some for these reasons.

I also picked sane defaults for growing conditions. The formulas diverge if you get too far out of plant growing range. You should be very safe if you are within about 40 to 150 degrees F and 20% to 90% humidity ranges (those are just guesses). Atmospheric pressure was picked as sea level and doesn't really affect anything until about 5,000 or 8,000 feet depending on how accurate you want to get. If extreme conditions apply to you, there may be other FAQ entries with the entire full blown set of pressure/temp/airflow/humidity parameters.

Design
1) Start at the beginning and design this right! Before you ever buy or cut anything for your new project, determine the highest temp (in F) your intake air will ever be when lights run. Get a thermometer and measure it to make sure you have a good value. Call this T(inlet)

2) Use these formulas to determine difference in temp you can tolerate. 81F (27F) is about the optimal for growing, 86F/30C on the higher end.

Tdiff = 81F - T(inlet) (English)
Tdiff = 27C - T(inlet) (Metric)

3) Add up wattage for all power in your box. Lights, pumps, heaters, humidifier, radio, coffee pot, whatever. Add it all up and call it Watts. This will make your number worst-case and therefore a conservative value.

4) Compute the absolute minimum fan power you will need using the following formulas. This is the minimum fan rating you must have to achieve your temperature goals. You will have to increase fan power to compensate for duct constrictions, small inlets, carbon scrubbers, screens, or other items that block airflow.

CFM = 3.16 x Watts / Tdiff (English)
CMH = 2.98 x Watts / Tdiff (Metric)

The formulas are almost identical, due to the counteracting effects of converting airflow from CFM to CMH, and converting temp from Fahrenheit to Centigrade.