When we get right down to it, we are all leaders at some point. It's situational, and sometimes we don't have any choice in the matter. Leadership may be thrust upon us, but influence is entirely earned. I would argue that being influential is more important than being a leader. Jane Fraser, I think, feels the same way :).
Influence is not force, it's not manipulation, and it's not gamesmanship. Sadly, many people feel that that is what influence is. Certainly we can use those attributes to gain influence, especially if we hold power over others (titles are somewhat irrelevant in real influence. People who respect you will walk though fire for you regardless of your title. People who don't respect you may put forward a brave face and pay lip service, but behind your back, they will undermine you (or at the most benign level just ignore you).
So how can we get beyond the counterfeit influence? I'm going to borrow a Coveyism (meaning I'm stealing from Steven Covey, he of the "7 Habits of Highly Effective People" fame). To have genuine influence, we need to build "emotional capital" with our associates and peers. That emotional capital needs to be developed at all levels, not just with upper management. One sure way to develop emotional capital is exchange information and experiences. In my world view, that means being willing to not be the sole proprietor of my job. IF I know how to do something, I try to make HOWTO docs that spell out how I do it. Some might think that would be a detriment, i.e. where's the job security? Fact is, my job is not secure without emotional capital, and sharing my knowledge develops that capital. It also frees me up to explore other areas, safe in the knowledge that I am not the silo, you do not need me to do that thing, because i've shown many others how to do it.
Persuasion is a fine art, and it's one that is often honed with many experiences of not being persuasive. Persuasion is, in my opinion, much easier when you are dispassionate an objective, rather than passionate and enraged. Making a clear case as to why you should be listened to takes practice and experience, and developing a track record of knowing what you need to do. Over time, another aspect of persuasion gets developed, and that is respect. Respect is earned, often over long periods of time, and unfortunately, it's one of those resources that can be wiped out in a second.
Influence often comes down to timing. Unless the building is on fire, in most cases, timing and understanding when people are able to deal with what you need to present and persuade about helps considerably.
Over time, you are able to develop trust, and that trust is the true measure of your emotional capital. If your team trusts you, if you have made the investments in that emotional capital, they will go to bat for you, because you have proven to be worth that trust. Like respect, it's a hard earned resource, but it can be erased quickly if you fall short or prove to not be trustworthy.
Being able to work with the team and help the team as a whole move forward shows to the other members of the team that you are worthy of respect, trust and that you deserve the influence you hope to achieve. Note: leadership is not required here. You do not need to be a leader to have influence. in fact, as was shown in an earlier talk today, the leader or first adopter has less influence than the first follower does. That first follower is showing that they have faith in the first person's objective, and by putting themselves in the position of first follower, they are the ones that influence more people to sign on or get behind an initiative.
A key component to all of this is integrity. It may not be easy, you may not always be popular, you may wish to do anything else, but if you keep true to your word, your principles and you own up to shortcomings or mistakes without shifting blame, you demonstrate integrity, and that integrity, if not always outwardly praised, is internally valued.
Active listening is a huge piece of this. To borrow from Covey again, "seek first to understand, before you try to be understood". It's often hard to do this. We want to be right, and often, we put our emphasis on being right rather than being informed. We all do this at some point. Ask yourself "are you listening to what the speaker says, or are you too busy rehearsing the next thing you want to say?" If it's the former, good job. If it's the latter... might want to work on that ;).
Ultimately, influence comes down to reliability and dependability. People's perception of both of those is entirely dependent on your emotional capital reserves. You are not reliable and dependable, you demonstrate reliability and dependability. Over time, people perceive you as being reliable and dependable, and the relationships you foster help determine how deep that perception is.