How long does it take to construct a nuclear power plant?

It depends where. In the U.S., it takes several years, mostly because of all the environmental studies and impact statements, permits and other government paperwork. Also, in the U.S., each one has some level of custom engineering. Also, unions slow down the work considerably. (I would not have made that last statement before I worked with some engineers who had been involved in building a nuclear power plant. They told me that the Plumbing, for example, took between 2 - 3 times as long as it would have with non-union plumbers, and there is A LOT of plumbing in a nuclear power plant.)

A conventional plant without any site-specific engineering or red tape could be built in less than a year.