Most home furnaces have a junction box where your 110V connection is hard wired and protected behind a cover. It's a pretty straight forward project to modify this with a plug and socket so if using a portable generator you can simply unplug it from the home's wiring and connect it with a cord to the generator. Just be aware air conditioning and electric baseboards (and water heaters) are usually the killer consumers and too much for smaller units, but heating systems that use oil or gas don't really draw much.
A full home system like highfive mentioned is first class of course, but the portability and convenience of a quality smaller unit should be pointed out. I love my Generac too, but its my Honda 2200 that helped me build a cabin in Vermont and has powered chainsaws and log splitters producing who knows how much firewood. Even just the ability to use my leaf blower at the extremities of my property without a 1/4 mile of cord.....lol
A smaller generator with a little thought on how to easily connect it goes a long way.