A bit of blue sky speculation

Comin, coming.. ! The basic principles are really pretty simple. The main power source is, of course, the nuclear reactor. Without getting too far into the weeds, a reactor generates heat by splitting Uranium atoms. Oddly enough, nuclear reactors are not at all hard to control, and have a great virtue over a fuel fired boiler in that they can go from idle power to full power very quickly. The heat from the reaction is transferred to water circulating through the reactor under considerable pressure, so it won't boil. However, it becomes radioactive in the process, and you don't want radioactive steam, so it in turn is circulated though heat exchangers which have normal water in them which is boiled by the circulating reactor coolant. This steam is then run through a steam turbine, which in turn spins your drive system (some is also used for auxiliaries -- turbogenerators for electricity, distillation units, etc.). The exhaust steam from the turbine is condensed by another heat exchanger, this time cooled by seawater, and the condensate is fed back to the heat exchanger by high pressure boiler feed pumps.

It's a completely closed system so far as steam production is concerned. Most earlier submarines used seawater directly in the condensors (and all surface ships do) but some later submarines use skin coolers, which are much quieter as well as not needing a through hull connection. Any makeup water is made by the distillers -- and any requirement for makeup water is a cause for considerable concern by the chiefs in charge -- it shouldn't be there! At the pressures involved, a leak is a potential catastrophe. The water used in both the reactor and power output loops is incredibly pure.

Speaking of the chiefs, the safety and mission availability record for US nukes -- both submarines and surface -- is almost incredible. This is partly because of the engineering involved; the designs we use are all fail operational and have multiple safeties. They aren't cheap. But a tremendous amount of credit must also be given to the men and women who crew these boats. They are very highly trained and absolutely dedicated to their work. The washout rate in training is very high -- but once aboard, the reenlistment rate is among the highest in any service.

That's sort of a thumbnail for US boats. There are a few other reactor designs used; a few actually do permit boiling in the reactor (common enough in land based units) and a very few very high performance compact units use liquid sodium as the reactor coolant. The US tried that but I believe on only one boat, early on. The Soviets did use it on some of their very fast attack submarines. There are real problems with it, which is why we don't use it (the Soviets were a little more casual...). There are other reactor designs which are fail safe -- in particular, a loss of coolant accident will cause the reactor to shut down -- but they aren't used at sea.

Hope this helps some.