From what I understand about nuclear reactors, there are two things mediating the reaction: Fuel (usually Uranium), and Neutrons. So adding either, or removing the absorbtive medium (usually graphite) will increase the rate of the chain reaction.
But I honestly have no idea
I suppose you could add more Fuel, but you don't really want to have to go into a working nuclear reactor every time you want to change it's power
A nuclear reactor is a chain reaction. 1 Neutron hits a Uranium (usually) core, splitting it into two smaller cores, and releasing
several (3/4) new neutrons. These neutrons can then hit new uranium cores.
The problem with this is that if all new neutrons would set about a new reaction, the number of reactions (= power) would increase exponentially. This would quite quickly result in too much power to handle, and then entire thing would explode/meltdown/become too hot.
Therefor, there are control rods to catch a certain percentage of the free neutrons, so that from the neutrons created in a single reaction, only 1 will start a new reaction. This is called "the k-factor is 1". That means the power is constant.
To increase it, you temporarily remove the control rods (you lift them up a bit), the k-factor becomes larger than 1, the power starts increasing, and once you reach the desired level, you lower the control rods again, the k-factor will be 1 again, and the power will be constant (but higher).