If you don't have a volt/multimeter, you can always try using a spare LED as a quick and dirty one to see if you're even getting power to the atomizer connection. Just briefly touch the leads to the center post and the outer sleeve. If it doesn't light, reverse the polarity of the LED to make sure that's not the issue. If it doesn't light then you're not getting enough power.
This can't tell what voltage you're getting, but will essential act like a continuity tester, and even if the power blows the LED (you can always install a resistor in series to prevent that), LEDs are much cheaper than buying a multimeter for a one-time use.
A multimeter is great to have, but not necessary if you're just looking to see whether you've got power, just for measurements.