Ok, let's go through this slowly. Your boiler is hooked up to your circuit breaker box. You need to buy a portable breaker box, that is specifically designed to handle generators. The electrician will hook the portable box up next to your home circuit breaker and connect the relevant breakers you want to have juice when you use your generator. He/She will also hook up a plug to the outside or your house that connects to the portable circuit breaker. Here is how it works. When you lose power, you hook up your portable generator to the plug, through a cord that is usually included. You then go to your portable breaker, and flick the switches from Line to Gen and it will automatically draw power from your generator. The beuty of this set up is you are given multiple switches, and you don't have to provide power to all of them, just the ones you want. For instance, I have a dedicated switch for boiler, then for refrig and microwave, then one for my basement that has my tanks.
I hope that answers your questions. Running the boiler shouldn't need alot of energy.