How do you determine the current that your system draws?

The best way is to measure with a current meter and an adjustable power supply (usually the current meter is built into the power supply). Set the power supply to the highest voltage that the system is rated at and measure the current, then set the power supply to the lowest voltage that the system is rated at and record that current. Adding a measurement half way between the two will give you an idea of where the lowest power consumption point is (power is voltage times current). The idea is that you want to design your pack so that the voltage swing of the batteries (see below) is adequate, and where the power consumption is the least. Some systems will show approximately constant power consumption no matter what the battery voltage is, and some will have a sweet spot where the power is lowest. 

If a variable power supply is not available, chart the current versus the voltage of the battery during a discharge cycle.

If making actual measurements is not possible, use the system data sheet, or the "boilerplate" sticker on the back to find the rated wattage or input current. This will usually give you a high estimate, or a peak value.