To edit a page, just click on the "Edit" link at its bottom. Depending on whether the page is text or other file, you will see a text editor or upload form. There are also two fields, one for comment, where you can type a short summary of your change, and another one for your name.
If you don't give your name, your IP address will be used instead. Once you provide a name, it is remembered in a cookie on your computer, so you don't have to type it over and over again when editing other pages.
If you edit a page several times in a row, your comment will be remembered. If you don't change it, only the last edit will appear on recent changes list – this way you can fix your typos without cluttering the wiki with small changes.
Once you make all the changes you wanted, or select the file to upload, press the "Save" button to have everything written to the server. If your press "Cancel", all your changes will be forgotten.
If you double-click on some text or title on the wiki page, the page editor will open already scrolled to that fragment – this is useful for correcting typos and improving wording.
You can also edit all the files directly, with your favorite editor of choice. This has the advantage of being able to edit the images and other binaries, provided you have an editor for them. Just don't forget to commit your changes with mercurial after you edit them from outside the wiki.