What needs to be done?
Report Bugs
Download builds. All you have to do is use it as your everyday browser and mail/news reader. If you downloaded a build with Talkback, please turn it on when it asks. Talkback reports give us really valuable data on which crashes are the most serious, and how often people are encountering them. And all you have to do is click "OK". If you find something you think is a bug, check to see if it's not already known about, and then please follow the bug submission procedure.
Quality Assurance
Getting involved in testing doesn't require knowing how to code, although a little knowledge of HTML is helpful. Being involved with QA is good for people wanting to get more familiar with Mozilla, and there's a strong community. More information available at the Mozilla Quality pages
Fix Bugs
Is there some bug that really bothers you? As well as reporting it, feel free to fix it. Fixing bugs in Mozilla is far easier than in many other applications, because you can fix bugs (such as those in our cross-platform front end, written in XUL, our XML-based User-interface Language, CSS and Javascript) using only the build you are running right now. There is no need to set up complex environments, or compile anything. We've even written a tool to make it really easy to get started - Patch Maker. So, if you've written web pages, you can hack on Mozilla.
Docs and Website
The website is currently being totally rewritten, and any help would be greatly appreciated. Mozilla could also do with all sorts of documentation - see the Mozilla Documentation Project. The nerve centre for this activity is the newsgroup netscape.public.mozilla.documentation
Interacting with Mozilla Contributors
Mozilla developers tend to hang out on IRC. If you've installed Chatzilla, getting connected is easy. Otherwise, fire up your favorite IRC client and connect to irc.mozilla.org:6667, #mozillazine (a friendly channel belonging to MozillaZine.) The development channel is #mozilla, although please note that people are trying to do work in this channel, so please don't ask support questions there. Other ways to get involved include reading the newsgroups and status updates.