Yes! Yes, of course you can. Wikipedia is a collectively-written encyclopedia, and that means anyone, anywhere should be able to add to and edit it. (With good intentions, of course.) And you can get to instructions about how to do it from the “anyone can edit” link on the site’s first page. The editors have provided a handy tutorial to walk you through the technical elements of it.
You need to know, though, that there are rules and guidelines for editing. Here’s the summary, from that tutorial page:
The goal of a Wikipedia article is to create a comprehensive and neutrally written summary of existing mainstream knowledge about a topic. Wikipedia does not publish original research: an encyclopedia is, by its nature, a tertiary source that provides a survey of information already published in the wider world. So we require that information be verifiable in reliable external sources. Ideally, all information should refer to reliable outside sources, using citations. When adding content and creating new articles, an encyclopedic style with a formal tone is important. Instead of essay-like, argumentative, or opinionated writing, Wikipedia articles should have a straightforward, just-the-facts style.
Wikipedia does not have many hard-and-fast rules; but policies, guidelines, and formatting norms are developed by the community to describe best practices, clarify principles, resolve conflicts, and otherwise further our goals. All editors are expected to follow general social norms. The Wikipedia community comprises people from many countries and cultures, with different views, perspectives, opinions, and backgrounds; in some cases these vary widely. Editors should treat each other respectfully, work together collegially, and avoid behaviour that is regarded as unacceptable, disruptive, controversially one-sided, or cheating the system.
There you have it! Go forth and contribute. Wikipedia particularly needs contributions from more women and other people who are not “technically inclined, English-speaking, white-collar men living in majority-Christian, developed countries in the Northern hemisphere.”
And it’s not just Wikipedia you can edit. The Wikimedia Foundation, which hosts Wikipedia, has a number of other projects. You can also contribute to images or documents in Wikimedia Commons (which I used extensively to find the images used on this site and my book); contribute or find books and other learning materials on Wikibooks or Wikiversity; or contribute to free news reporting on Wikinews.
If you’re still worried that Wikipedia is unreliable, here’s an interesting review of that concern, on Wikipedia itself, including the results of studies on Wikipedia’s accuracy. Again, as I said in the book, Wikipedia is best used as a jumping-off point for finding other research, rather than a source itself.