It may sound silly, but the most important part of being a leader is, well, leading. Leading doesn't mean being the boss and telling people what to do. Leading means steering and supporting the effort, being at the forefront of the effort, and showing people in the team the way forward. Leading means knowing where you are going, knowing how to get there, and heading off in that direction. Leading means being the one others want to (not have to) follow to get to the goal.
So, how do you lead? Certainly if you are in a position of authority it helps as you will get the team to follow you because of the role. But real leadership is not about being the boss, it's about having people wanting to follow you because you inspire them, know what you're doing, and know how to get where you are going. Followers want to get there, too, but they perhaps don't want to be at the forefront or they don't know how to lead.
To prove leadership doesn't mean management, here's an example from a team that was put together to accomplish a particularly tricky bit of software engineering. The team was made up of six people, and the manager didn't appoint a team lead, just told the team where they had to get and when they had to get there. The details of how to solve the tricky engineering problem, how to manage the development process, and how to ensure the product was solid was left to the manager-less team. The team did what such teams almost always do: they had a meeting! In the meeting there were six opinions on how to get where they had to go, and what it would take to get there. The first order of business was defining the solution, which was pretty easy since it was already laid out. Then, the second order of business was to figure out how to get there. Of the six different solutions, a group discussion narrowed the six solutions down to three pretty quickly on either technical grounds or based on the complexity of the solution. The six engineers started discussing the three solutions that were left, and one more was easily eliminated. But the last two had equal numbers of proponents and would require much the same amount of work to finish, and invoke just about the same amount of risk to the project success. What was interesting about the discussions was that although there was no manager for the team, one person was more obviously taking the front in the effort, steering the discussion to its conclusion without being pushy or demanding. As the meeting went on, more and more of the team started to defer to that one person. Not because they were technically the best, but because they approached the issue logically and helped keep the discussion on track and progressing. In the end, that one person was on the losing proposition's proposal, but that didn't matter because they were more interested in consensus than "being right" . That one person became, almost without effort, the leader of that team in the space of two hours. After the meeting, the discussion about why that person was the lead centered around the person's ability to keep the discussion moving, the goal in sight, and the participants in the meeting all equal. This is a prime example of natural leadership: it had nothing to do with being a manager, being the best technical person, or even being the most organized. It was about seeing the goal, helping the team see how to get there, and then, once the process was defined, helping the team stay on track. In the end, it was about the respect the rest of the team had for the one person that made them him the leader. And, in fact, he was the leader because he led the team in that short meeting, and in the weeks to follow maintained that role even though his team were all peers.
Of course, to be a leader, you have to know what to what you are leading the team. That means having a clear idea of the target. Whether you are the manager or a peer, if you don't understand the target, it's difficult to help steer and motivate the team to get there. So, a clear understanding of the target, what it is supposed to be and do, and how long you have to get there is key. If you don't understand the target, ask questions of the person who is setting the target and deadline. You need to know as much as, if not more, than everyone else on the team about the goal. To help get the team to that target, it helps (but is not necessary) to be a technical person too, and understand the issues involved and how to get to the target. It is possible to be a passive (non-technical) leader in a technical team, but it does help to know the technical subject inside out. Knowing the technology gives you a heads-up towards the respect you need to be a leader. And, to lead, you have to make sure the team discussions are kept on track and don't go off on tangents, that technical issues are solved, that assignments to team members are doled out, tracked, and managed, and that progress towards the goal is achieved. All that without being pushing or having actual authority if you're not the manager. It's not easy to do that, of course. If it was, everyone would be a leader!
You know leadership when you see it. People listen the a leader, although a leader is always careful to listen more. A leader is one who people want to work with and help attain a goal with. A leader is someone who knows where to go, and usually knows how to get there, and can get there without time wasted in detours. A leader is someone whose opinion is sought, naturally, and who is able to think logically and clearly and help eliminate extraneous thoughts and matter. A leader is someone who is willing to take the front role, take the blame when things go wrong, and share the credit with the team when things work out. A leader is not a self-promoter, egotistical, or necessarily better in any way than everyone else. They just are the one who the others will listen and look to, and follow.
So, leaders lead. Not because they are management, but because they have the ability and the buy-in from their peers and teams. It all comes down to respect from the teams for the leader. Without that respect, there is no leadership, just management.