To make it a little more complicated: from my (very limited) experience it really depends on the type of double exposure you want to make whether or not you have to adjust the exposure times.
I would categorise double exposures in two rough categories: (a) non-overlapping exposures and (b) overlapping exposures. (a) is quite easy to explain: one example would be that you basically cover the left half of your image with black cardboard that you hold in front of your lens, make the first exposure and afterwards cover the other half of the image to make the second exposure. In the case of (a) you wouldn't adjust the exposure times at all because you need the correct amount of light to expose both halfs properly. One example for (b) would be if you take a picture without covering any part of the lens and make the first exposure and then make another exposure to combine both images. In this case you basically need half the amount of light from the first exposure and half of light of the second exposure to get a full amount of light for a correct exposure. This can be done by exposing twice and correcting the measured exposure by EV -1 as Kai-san said. If you don't have an EV dial, simply set the ISO to twice the original ISO to get 1 stopp of underexposure. However, this only works if the contrast between objects is not too big. If you have tons of black areas in both exposures, it might be wise to expose with EV -1/2 or even EV -1/3 (as long as the overlap of light objects is limited).
That being said, this is only a rough guideline that I thought up while playing with double exposures. It may very well not work for all scenarios. However, I wouldn't make double exposing into rocket science with respect to exposure times. Play around with exposure and let the results surprise you. In my opinion, what's more difficult than exposing properly is composing double exposures that actually look interesting.
It often works nicely to place something light that's surrounded by dark areas from the first exposure into a dark area of the second exposure. However, it's really, really hard to visualise what the result will look like before you take the shots. So the fun part will be the trial and error phase and finding recipes for double exposures that you find interesting. I'm very sure that you'll have a lot of fun.