Teach Us Your Skills
If you're not exhausted yet, or those other two ideas didn't really appeal that much, the library needs you to impart your skills to other members of the community, but also to the staff. In public libraries, we serve both the most up-to-date gadget wizards and people who are far more comfortable with a manual-action Remington typewriter than a word processor.
Here's another secret of the public library: The staff probably doesn't know enough about enough to actually be knowledgeable about everything. However, we're really good at being able to find that knowledge quickly and accurately, whether in printed or electronic form. Search engines are great at returning results, librarians are great at returning information. The algorithms can sort spam from wheat from chaff, but the people can select which of the results will be most useful at that moment in time.
Knowing how to find knowledge, however, is different than having that knowledge at hand, and is very different than the knowledge that comes from doing something for many years. Most of us can cook from recipes, myself included, but if you handed me a bunch of ingredients and put me in a kitchen, saying, "I'll see you in an hour for something delicious", if the food was edible by the time I was done, I would call the whole thing a success. I don't have the knowledge and practice that allows me to see complete dishes from ingredients. Similarly, if you put me in a room with a computer and a tutorial for a language and asked me to build a complex program, I'd try, but I don't think it would be very elegant. If the program ran at all. A librarian's expertise is in finding things that are organized in a system (preferably a logical one), and in having a broad base of knowledge to be able to get people started on their own pursuits and endeavors. Passionate people who want to learn more or hone and perfect their craft, however, will rapidly outstrip the expertise that librarians have, unless the librarian is equally as passionate and expert at that thing. The likelihood of that, however, is tempting the Random Number God in ways that rarely end well.
For this aspect of becoming an open-source institution, we need from you a willingness to teach or mentor or be there as a peer advocate. If you have a computer users' group that meets in library space regularly, invite one of the staff in during a meeting to see what's going on – if the library knows what you are doing and when you meet, they can begin to see you as more than just a scheduled appointment on their meeting room calendars. You become a resource that can be tapped to help someone else. Or, if the library wants to put on a program, they may ask you to provide expertise to shape and perform a program that people will get a lot out of and want to come back for more.
In some libraries, the staff will approach you and try to get to know you proactively. In a lot of other ones, the staff will need you to approach them, because they're already pressed for time as it is between collection work, public service at the branch, outreach to the community, fiscal decisions, programming, and the work of the library that goes on away from the places the public sees. They want to be engaged with all of you, collaborating with you, and trying to make their space and collections the very best they can be for you (and everyone else). If your public library isn't actively trying to recruit you, volunteer yourself to them.