When I do hydrostatic tests on steam locomotives (full size), the safeties are removed and capped off, and the whistle if mounted on the dome is removed or if a shutoff valve is present it is shut. Water (warm if available) is added until it flows out the top of the whistle or safety valve pipe nipple.
I connect my hydro pump to this nipple and if the water is cold, then it warmed by a light fire. Warming of the water is done so as not to shock the boiler due to excessive air when pumping it up.
The hydro pump is connected to a water source which keeps it full. Make sure the feedwater checks are closed.
Two trains of thought here are pumping up to rated pressure, checking for leaks in the firebox and smokebox ends, and general observation around the locomotive.
On live steam locomotives, the theory is to pump the boiler up to 1.5 times the rated pressure.
I am sure others may chime in on this as to what they may or may not do differently. I would never use compressed air to hydro the boiler however.
The picture shows the initial preparation for a hydrostatic test being done on former High Country #8 which I performed back in December. The hose has filled the boiler and the blower on the stack is creating a draft for a wood fire to warm the water. This locomotive passed and is being readied for service once again.