You are correct here. Boilers are fired by either the heat coming from a nuclear reaction or by the burning of coal, oil, natural gas, or even wood.
Boilers boil water. That water is above freezing as a result. The resulting steam is sent through plumbing to perform some work such as turning a turbine or shoving on a piston. That work reduces the energy in the water, allowing it to cool. It's still steam, but ready to condense out as liquid water (which takes a bit of time). Condensers give it this time. That water is not returned to the boiler and injected using a double venturi injector. It's a pretty simple system, really. No moving parts (other than the turbine. Even the injector has no moving parts. The boiler itself is the pump. In one form or another, Man has been using this exact system since the steam locomotive was popular.
Earlier steam engines used valves that WERE moving parts, and valves were used on steam locomotives as well, but these operate in a steam or hot water environment. Turbines don't need 'em.
You can start a steam engine even if you begin with all the water totally frozen (assuming the plumbing isn't damaged). The return lines are melted with the steam right there inside the plumbing. It takes awhile of course, but it will melt all the water in the lines and function as always.