Select the clip and go to the 'Effects' tab >> 'Video effects' >> 'Brightness/Contrast'.
You'll have to experiment with the settings to get what you want. I'd suggest adding contrast so that the blacks don't get washed out to grey. Don't worry about making a mistake -- you can undo.
Notes: You didn't say which version of MEP you are using so your menu might look a bit different. Also, though a search for 'brighten' doesn't find anything in help file, 'bright' or 'brightness' would have given you this information.
If Carls suggestion does not do what you want, try using the Selective brightness (Gamma) slider shown in Carls image.
Depending on how dark the video is and how much you want brighten it by, the quality may not be very good - especially if the video is quite dark, you will introduce even more camera noise. See the example below - the Gamma was increased to 100 for the second half - as you can see there is a sort of shimmer effect - this is 'camera noise' that has been amplified - also note the shift in colour.
I almost never use the Brightness slider. Selective brightness (Gamma) gives a more pleasing result. Once you have increased the slider a little, toggle through the Drop down next to the slider and see the effect from Lows, Mids, Highs. Lows will lift the blacks considerably without over exposing the lighter areas. After each selection you may need to tweak the slider more or less.