So the way it works is this. Natural uranium is a mixture of two isotopes- U-238 and U-235. Only U-235 is really useful, because when a neutron hits it, it goes *pop*, falls apart, and emits a few more neutrons. U-238 just swallows the neutron, decays into neptunium and eventually becomes plutonium- but it doesn't emit much energy in the process.
The problem is, then, that U-235 is really scarce- it only comprises less than one percent of natural uranium metal- so if you're to have a fission chain reaction you either need to make pure (what we'd call weapons-grade, or high-enriched uranium) U-235 with as little U-238 in it as possible, or alternatively, give every neutron the absolute best chance of hitting a U-235 atom and causing it to go pop.
Why is this hard? Well, an atomic nucleus is a bit like a drop of water; if you fire a neutron into it at high speed, it won't stick to it, it'll just go straight through. And guess what, the neutrons emitted by a fission *are* going at a fair old lick- fast enough that they don't cause many fissions. This is a problem.
In order to make fission happen at all, therefore, in your big pile of natural uranium, you need a moderator. What this does is to slow neutrons down- by bouncing them around between atoms that are unlikely to absorb them, like deuterium or carbon, so that when they eventually hit a U-235 nucleus, they're going slow enough that they'll stick.
The name "moderator" confuses people a lot. For some reason they think of "moderating" the speed of the reaction, when in fact they allow the reaction to occur in the first place! In some reactors, like British Magnox and AGR reactors, solid bricks of graphite are used as moderator, and in some, like the Canadian CANDU reactor design, a large stainless steel structure full of deuterium oxide (heavy water) is used. In still others, a less efficient but much cheaper fluid- ordinary water- is used, but these need slightly enriched fuel because the moderator absorbs too many neutrons to work well with natural uranium fuel.
Finally, of course, there are reactors like IFR, PFR and DFR- fast breeder reactors- which use no moderator at all. These reactors have to use extremely high enrichment, because most of their neutrons pass straight through the fuel without causing any fission. Technically, a nuclear bomb is a fast reactor, though it involves maintenance issues...
The reaction is *not* controlled using the moderator, in most reactors; indeed, taking the moderator out will stop most reactors- this is one of the safety systems used in water-moderated reactors, since if the coolant disappears the reaction stops. The reaction is controlled using carefully adjusted concentrations of boron and gadolinium in the coolant, and also by using cadmium (and similar material) rods which are drawn in and out of the reactor, absorbing neutrons. These "control rods" (sometimes "drums", on the outside of the reactor) are not part of the moderator.
Hope this clears things up!