Like most cultures without a money economy, hackerdom runs on reputation. You're trying to solve interesting problems, but how interesting they are, and whether your solutions are really good, is something that only your technical peers or superiors are normally equipped to judge.
Accordingly, when you play the hacker game, you learn to keep score primarily by what other hackers think of your skill (this is why you aren't really a hacker until other hackers consistently call you one). This fact is obscured by the image of hacking as solitary work; also by a hacker-cultural taboo (gradually decaying since the late 1990s but still potent) against admitting that ego or external validation are involved in one's motivation at all.
Specifically, hackerdom is what anthropologists call a gift culture. You gain status and reputation in it not by dominating other people, nor by being beautiful, nor by having things other people want, but rather by giving things away. Specifically, by giving away your time, your creativity, and the results of your skill.
There are basically five kinds of things you can do to be respected by hackers:
The first (the most central and most traditional) is to write programs that other hackers think are fun or useful, and give the program sources away to the whole hacker culture to use.
(We used to call these works “free software”, but this confused too many people who weren't sure exactly what “free” was supposed to mean. Most of us now prefer the term “open-source” software).
Hackerdom's most revered demigods are people who have written large, capable programs that met a widespread need and given them away, so that now everyone uses them.
But there's a bit of a fine historical point here. While hackers have always looked up to the open-source developers among them as our community's hardest core, before the mid-1990s most hackers most of the time worked on closed source. This was still true when I wrote the first version of this HOWTO in 1996; it took the mainstreaming of open-source software after 1997 to change things. Today, "the hacker community" and "open-source developers" are two descriptions for what is essentially the same culture and population — but it is worth remembering that this was not always so.
They also serve who stand and debug open-source software. In this imperfect world, we will inevitably spend most of our software development time in the debugging phase. That's why any open-source author who's thinking will tell you that good beta-testers (who know how to describe symptoms clearly, localize problems well, can tolerate bugs in a quickie release, and are willing to apply a few simple diagnostic routines) are worth their weight in rubies. Even one of these can make the difference between a debugging phase that's a protracted, exhausting nightmare and one that's merely a salutary nuisance.
If you're a newbie, try to find a program under development that you're interested in and be a good beta-tester. There's a natural progression from helping test programs to helping debug them to helping modify them. You'll learn a lot this way, and generate good karma with people who will help you later on.
Another good thing is to collect and filter useful and interesting information into web pages or documents like Frequently Asked Questions (FAQ) lists, and make those generally available.
Maintainers of major technical FAQs get almost as much respect as open-source authors.
The hacker culture (and the engineering development of the Internet, for that matter) is run by volunteers. There's a lot of necessary but unglamorous work that needs done to keep it going — administering mailing lists, moderating newsgroups, maintaining large software archive sites, developing RFCs and other technical standards.
People who do this sort of thing well get a lot of respect, because everybody knows these jobs are huge time sinks and not as much fun as playing with code. Doing them shows dedication.
Finally, you can serve and propagate the culture itself (by, for example, writing an accurate primer on how to become a hacker :-)). This is not something you'll be positioned to do until you've been around for while and become well-known for one of the first four things.
The hacker culture doesn't have leaders, exactly, but it does have culture heroes and tribal elders and historians and spokespeople. When you've been in the trenches long enough, you may grow into one of these. Beware: hackers distrust blatant ego in their tribal elders, so visibly reaching for this kind of fame is dangerous. Rather than striving for it, you have to sort of position yourself so it drops in your lap, and then be modest and gracious about your status.