Ƿé onginnaþ mid þǽm ealra déoplicostan gecynd: Ádihtan þisne tramet. With the exception of very few protected pages, every wiki page has a link at the top that says "edit this page." This link lets you do exactly what it says — edit the page you're looking at. Sites such as these where anyone can edit anything are known as wikis.
Try it! In níƿum éagþyrele, opena þisses trametas sandboxe, and þá besting þone "ádihtan þisne tramet" bend. You'll see the source code for that page. Write something pithy or amusing, or just say hello. Then save it and see what you've done. There is more detail at Wikipedia:How to edit a page. You might want to open this in a new window, too, so you can carry on with the tutorial.
Whenever you want to experiment without worry, you can always do it in the Wikipedia:Sandbox. It's a "safe area" of sorts.
An important feature to start using now is Show preview, which allows you to see what the page will look like after your edit, even before you save. Try making an edit in the sandbox, then clicking the show preview button. We all make mistakes, and this lets you catch them immediately. If you make a habit of using Show Preview before saving, you'll save yourself and other editors a lot of trouble. It also lets you try out format changes without actually changing the article until you're satisfied.
This is especially important if you think you may be making other edits on the page. It is a good idea to just Save once, to keep the page history uncluttered. Saving less often is also a way of avoiding edit conflicts, which occur when two editors try to change a page at the same time. However, when you change large amounts of text you should consider doing this in successive steps (e.g. one paragraph at a time) so that others can follow your edits more easily.
If you are logged in as registered user, you can mark an edit as minor by checking the appropriate box before you save. This is used to show others that your edit is not something substantive. There's no strict guideline on when to do this, but certainly spelling corrections and minor format changes like adding a space or a wikilink are minor edits. In other words, changing the presentation is generally minor, but changing the content is not. When in doubt, don't mark the box. For a more detailed discussion, see Wikipedia:Minor edit.
Before you hit Save, it is considered to be good practice to enter a very brief summary of your change(s) 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.