A boiler replacement runs in a fixed order, and the order exists to protect the house, the water, and the gas line. Before the work starts, read the installer's written scope and confirm that the permit and inspection steps are named in it. The details will vary with the boiler type and the local code, so the installer's scope governs the job.
First, the old system goes cold and isolated. The electrical supply is switched off at its disconnect, and the gas supply is shut at its valve. The water supply to the boiler is closed, and the system is allowed to cool fully before anyone opens a fitting.
Next, the system is drained to a safe point and the old unit is disconnected in a planned order. The gas connection, the flue or vent, the water connections, the relief valve line, and the electrical supply each come off on their own step, and each connection is checked off before the next one is touched. Keep a note of what was connected where, because the new unit has to match it.
Then the new boiler is set level, the gas and water connections are made, the flue is joined and supported, and the electrical supply is restored. The system is refilled slowly, and air is purged from the radiators or zones until water runs without it. The expansion tank and the relief valve are checked as the installer's scope names them.
After that comes the first firing. The burner is lit under the installer's supervision, the flue draft and the gas connections are checked for leaks, and the controls are tested against a real call for heat. Run each zone so you can see that it heats. Watch the pressure as the system warms, and make sure it settles within the range the installer marks. Ask for the final checks to be written on the sign-off sheet, with the pressure readings, the zones tested, and the controls confirmed.
Keep that sheet with the boiler paperwork. It is the record of how the job was done, and it is the first place to look when a later service visit asks what changed. For the typical service life of this system and when to start planning, see the boiler page on this site.