Using nuclear reactors the size of a trash can to power a colony on the Moon

You can read about that here - NASA is working on a series of small nuclear reactors that size that are capable of producing enough power for the equivalent of eight houses on Earth. The article gives details on how they work so I won't go over that here.

Nuclear power is a bit of a weird issue since it was so ostracized in North America for so long due to environmental reasons, while at the same time France has focused mainly on nuclear power...also for environmental reasons. North America has certainly gone overboard in its opposition to nuclear power. It's similar to airplanes, which are far superior to other types of transportation most of the time and almost always perfectly safe, but when disaster strikes it makes the front page. At the same time power sources such as coal and gasoline don't produce these disasters, but at the same time kill far more people every day through polluting the air and the worsened health and greater prevalence of disease that comes along with that.

Back to NASA - luckily the Moon has peaks of eternal light at the poles where nonstop solar power is available, so for the very first settlements on the Moon a nuclear power source will not strictly be necessary. You can see one of these peaks of eternal light in the image on the right (the red circle).

One other good reason to begin colonization from a location like that though is also psychological, so it's not just the electricity issue. It's possible that humans could get quite depressed during the 14 days of night that the Moon experiences. In the beginning when the colony is quite small and desolate, if it were to be in a lower location, those in the colony might begin to dread the approaching night as day began to draw to a close.

Then again, night is also when the Earth is brightest in the sky (some 70 times brighter than the full Moon here) so perhaps it wouldn't be that bad. Either way, having access to the peak of eternal light can only be a plus.

Edit: you can also see a discussion on the topic on the space.com forums here.