Voltage divider = two high value resistors, in series, connected between two points. At the point between these resistors, the voltage is equal to the ratio between the value of the two resistors. So if you have a cap you expect to be up to 12v, you might put a 20k on the high end, to a 10k resistor, then to the low end (presumably the shared ground). At the point between those resistors, the voltage will be 1/3rd of the voltage between the two ends. Much more information available online.
Yes, it will drain the capacitor if you have to use the voltage divider. The extent to which this will be a problem depends on what you're doing, how big the capacitor is, etc. If it's max 5v, you can measure it directly with the arduino, and this will not drain the capacitor significantly.
What exactly are you doing?