Much like the old "Take my wife...PLEASE," the theory in having your authority respected is that asking people to do it often turns the whole respect thing into a joke.
When you encounter someone--in an elevator, in a work group, on a basketball court pick up game (yes, I play basketball. I don't play, you know, well, but I do play it)--you have to make a judgment about how much you are willing to trust that person given the immediate circumstances: what you are doing, if it's together, if it's collaborative, if it has long term consequences, etc.
In an elevator, for example, the immediate concern is not collaborative nor long term, but is certainly important and immediate: Can I turn my back on this person? This is because people in elevators traditionally face forward (unless you are a norm violating machine as mentioned in an earlier post). Whereas people looking to group for a pick-up game of basketball need to determine if they think that you can play at all, if you are an asshole (assholes tend to not play well with others) and put the more immediate safety concerns out of their mind. Finally, when working with someone (or someones) in a work group situation, you are not only looking at their ability to perform this task, you're probably also evaluating them for long term tasks, fit for your team or your personality, and, weirdly, some immediate safety questions pop back up--for example, does this person make you feel creepy? Because no matter how good he/she does the job, creepy is a trait that is VERY hard to overcome.
So why am I bringing up creepy people and basketball players? Because in each of the examples, you have to make a decision about how much you trust someone. Trust is the key, integral part that leads to respect. Its very hard to be untrusted and respected in the business world.
There are tons of books out there that basically say the same thing, which I'll sum up for you here: Respect is Earned.
Many of those books say things like "There are not shortcuts to respect," and "Respect comes gradually...it can take a long time." I'm going to suggest otherwise; you sink a few baskets and prove you can pass and be a team player, and the basketball pick up group is going to respect you. They are likely to remember you next week and pick you for their team, on purpose, because of that trust and respect.
While it's unlikely fellow passengers on an elevator will select you to stand behind them again, this metaphor does actually apply to the work situation. If you have to work with someone you don't know, and you treat them in a fair and open manner and, like the basketball player, share the ball and help others to score, you have respect. It's not in its full form; they won't follow you into battle or anything. But they might back your play in a safe environment. That's how respect starts.
These are all very controlled examples of trust and respect in a short period of time. The most common you'll run into is that you are sent to a completely different group to do something there related to, but not a standard part of, that group. For example, you're hired to lead an existing team of developers whom you've never met. Or, you are sent to another group to help them adopt a peer review process that your team did a great job with and management wants to reproduce the results.
Those people don't know you. They had a system in place prior to your arrival. It may have worked. It may have been dysfunctional. But it was theirs. You are new. You are unknown.
And the same things that garnered respect on the basketball court, in the elevator and in the base work group example still apply: be yourself, be trustworthy, perform well, share the credit, help other people look good. It can take days, not weeks (sometimes hours) to form at least the minimum respect from my basketball example...and that's what real respect and trust can easily grow on: stable, consistent behavior.
If you have to do things that make your trustworthiness questionable, be upfront about them. Be transparent. If the team succeeds at something, celebrate the team--don't give any credit to yourself. You do it right, and part of respecting you will be calling out your contributions; the quickest way to lose respect is to toot your own horn. Instead, toot the horn for other people. The important part, though, is MEANING it. Lying, as noted before, is the suck part of the job.
Everyone has something about them that makes them amazing to work with, even if that something is their absence. Seriously. I have had folks on my team who were pit bulls--the rest of the team had trouble working with them because they could not let go of something and they kept coming back on that topic aggressively, over and over again. But it turned out that pit bulls are very good to have when working with other teams that are shy about returning your emails or getting you the resources they promised. The pit bulls mentality can be useful to a team aimed in the right directions. Pit bulls, as a breed, are good dogs, and pit bulls in the office can become heroes. With the people as with the dogs, it's all in how they are trained and rewarded for their efforts.
Obviously, I could talk a really long time on this topic, and many, many people have devoted books to it. Sufficing to say, respect and trust are the foundation of a good manager and is the giant-blue-catch-bag-that-stunt-people-jump-into-to-avoid-being-hurt of the imperfect manager.