> The best route up is hitching your wagon to your bosses wagon. So yes doing some of his work will make him look like a hero, which will get him promoted, and he'll think who is his most valuable / productive underling, which will get you promoted. Hopefully you doing some of his work free's up his time to be more productive in other areas. If your boss is a lazy PHB (Dilbert), get another job.
This is called loyalty, and it only really works in certain kinds of endeavors, and then only certain organizations doing them. TV shows depict loyalty a lot, the thing I notice about these shows is that the stories are always set in "meat-grinder" sorts of fields, and then at the tops of those fields. Suits, set in a high-powered corporate law firm. Entourage, set in Hollywood. Loyalty as a major theme to a show isn't interesting to watch otherwise.
Everywhere else, an interested ladder-climber will always find that it's way easier and cheaper to change jobs than it is to move up in one. Hence the perennial advice to move to a city, where landing jobs is like shooting fish in a barrel for the ambitious. When you run out of steam at one company, get a fresh start somewhere else. Rinse and repeat until you're tired of moving around, then you can start the loyalty path.
It's important to note that the skills you need to convince someone else that you can do a job are way different than the skills you need to convince a power broker to bequeath you with additional responsibilities and the commensurate titles and prestige. It so happens that years of experience working in organizations gives you those skills largely through osmosis.
I like where I am now, so I investigated the possibility of sticking around and trying to move up rather than jump to another company. Even talked to my boss about it. But unless you're at a rapidly growing company, the opportunities for advancement just aren't going to be there and you might be waiting years for your turn. My boss specifically used the words, "you're comfortable" to describe my head space when he said he'd go around and ask if anyone else needed anything to do.
You and everyone else can have the best of intentions, but opportunity is limited and it's hard to make more of it. There's only ever a limited amount of money and perks to go around, and its often politically unfeasible to start rocking a boat by democratizing something that was previously held feudally.
Making the decision to stay at a company is giving up easy access to opportunity in exchange for security and stability. You can always unmake that decision by leaving, often times you can even unmake it the other way, companies will take people that leave back if they like them enough, but you and only you can decide what you want more out of your time on Earth.