How to make a discharge curve
Using a constant current load you'll get a nice curve if you plot the voltage over time. 

The C rating is given by the manufacturer as an indication of the safe maximum constant current draw from the battery.

Some searching turned up that it is standard to make the discharge curve over 20 hours. So this would be like 0,05C. I speculate that this will avoid some thermal effects, Because your battery would probably get hot from a 1C discharge. 

If it is a AA battery, set the current to about 100mA. AAA - 50mA 
if it is another kind of battery, guess or measure how much more or less volume it has compared to the AA battery, and factor that into the current. It is just a way of guessing capacity. So if the battery looks 4 times larger than a AA, set the current to 400mA. 

You can do this guessing because battery capacity is proportional to volume. 
After you've done this, you have measured the capacity of your battery, and you can make more precise measurements. Good luck