On the C&TS there are a few ways an engine is fired up, it all depends on the circumstances. There is no shop steam to feed to an engine being fired up. That being said, the most common way is to "borrow" steam from a hot locomotive to assist in the firing up of a dead one. If there is no steam available then the boiler is filled with water to about 1 inch or so showing in the engineer's water glass (no matter which procedure is used that is where the water level is set). Water is pumped in through the blow down. A bed of coal is shoveled into the fire box covering the grates. Some wood is thrown on top of the coal and then some coal on top of the wood (anytime a locomotive is being fired up from being cold this is how it is done, same with the next sentence). Diesel is then thrown in on the layers and is lit (sometimes the diesel can be dumped on some of the coal before it is shoveled into the fire box to help the fire grow if it's being contrary). An electric fan is placed on the smoke stack to create draft to get the fire burning. Time to get from cold to hot in this procedure is 3-4 hours.
Next, if there is an engine available to "donate" steam then the water level is set, fuels added, and lit as stated above. The difference is that the steam is used to run the blower and create draft instead of the fan. The steam also helps heat the boiler and build pressure. Time from cold to hot is 2-3 hours.
Now, there are a couple of variations on the above procedure. One is probably the best for keeping stress to a minimum while firing up the engine. That is steam is used from the donor engine to heat the boiler. All valves are closed except the blow down (and the one that admits the steam from the donor engine). As steam heats the boiler it condenses and flows out the blow down as cool water. As the boiler heats then the water turns hot and hot steam starts coming out of the blow down. At that point the steam from the donor engine is shut off and the blow down closed. Next the turret is closed and the monkey's tail opened, the steam turned back on and used to run the injectors (both are used) to fill the boiler to the afore mentioned level (the monkey's tail vents the boiler so injecting water is not fighting with pressure in the boiler). This heats the water which aids in reducing the stress to the boiler. Once the boiler is filled sufficiently, the steam is again shut off. Now the turret is opened and the monkey's tail closed. Now steam is fed into the boiler running the blower and the fire lit. Time from start to hot locomotive is about 2 hours or a little less. The other variation on this is to not heat the boiler with steam before injecting water which increases the time from cold to hot.
A couple of things to remember is that firing up a cold locomotive is normally done after needed repairs are completed, boiler washes are done, engine was taken out of service to reduce the service days, or after a winter's wait. So when firing up a locomotive there are constant checks on what could be leaking or of the repaired part (many repairs can only be done with the engine dead). Therefore, steam is normally used to pressurize the boiler before the fire is lit to check for leaks so they can be fixed before the fire is lit.
That is kind of a short synopsis of what goes into firing up a locomotive on the C&TS.