How do you know which ideal gas constant to use?

The ideal gas constant that you will use will depend on the units of the known quantities in the problem.
You will choose the R value based off of the units for the known quantities in the problem.
You will have values or be looking for values for:
V – usually in liters
T – Kelvin (convert to Kelvin if given Celsius or Fahrenheit)
n = moles
P = Pressure (atm, mmHg, Torr, kPa…)
The key is usually pressure.
For P in atm use R = 0.082057 atmL/molK
For P in kPa use R = 8.31446 kPaL/mol
For P in mmHg or Torr use R = 62.36367 mmHgL/molK
See the similarities in all of these? Just the pressure is different.
If the problem you are working on provides different units for the quantities, you can look up other R values here
http://en.wikipedia.org/wiki/Gas_constant