The most basic wiki feature of all is: Edit! With the exception of a few protected pages, every page has a link that says "edit." This link lets you do exactly that: edit the page you're looking at. Sites like these, where anyone can edit anything, are known as "wikis."
Just click the "edit" link on any page. You'll see the wiki code for that page. Add something fun and interesting (and relevant) then save it and see what you've done! Try it out in the Sandbox.
One important feature to start using now is the Show preview button. Try making an edit in the Sandbox, then clicking the Show preview button instead of Save changes. This allows you to see what the page will look like after your edit, before you actually save. We all make mistakes; this feature lets you catch them. Using Show Preview before saving also lets you try format changes and other edits without cluttering up the Recents Changes page and has a number of other advantages. Don't forget to save your edits after previewing, though!
Before you hit Save, it's considered good etiquette (or "Wikiquette") to enter a polite explanation of your changes in the edit summary box between the edit window and the Save and Preview buttons. It can be quite terse; for example if you just enter "typo," people will know you made a minor spelling or punctuation correction, or some other small change. Also, if the change you have made to the page is minor, such as a spelling or grammar correction, be sure to check the box "This is a minor edit" (this is only available if you have logged in).