To edit a page, click on the "Edit this page" (or just "edit") link at one of its edges. This will bring you to a page with a text box containing the wikitext: the editable source code from which the server produces the webpage.
After adding to or changing the wikitext it is useful to press "Show preview", which produces the corresponding webpage in your browser but does not make it publicly available yet (not until you press "Save"). Errors in formatting, links, tables, etc., are often much easier to discover from the rendered page than from the raw wikitext.
If you are not satisfied you can make more changes and preview the page as many times as necessary. Then write a short edit summary in the small text field below the edit-box and when finished press "Save". Depending on your system, pressing the "Enter" key while the edit box is not active (i.e., there is no typing cursor in it) may have the same effect as pressing "Save".
You may find it more convenient to copy and paste the text first into your favorite text editor, edit and spell check it there, and then paste it back into your web browser to preview. This way, you can also keep a local backup copy of the pages you have edited. It also allows you to make changes offline, but before you submit your changes, please make sure nobody else has edited the page since you saved your local copy (by checking the page history), otherwise you may accidently revert someone else's edits. If someone has edited it since you copied the page, you'll have to merge their edits into your new version (you can find their specific edits by using the "diff" feature of the page history). These issues are handled automatically by the Mediawiki software if you edit the page in your web browser.
When editing a page, a logged-in user has the option of flagging the edit as a "minor edit". This feature is important, because users can choose to hide minor edits in their view of the Recent Changes page, to keep the volume of edits down to a manageable level.
When to use this is somewhat a matter of personal preference. The rule of thumb is that an edit of a page that consists of spelling corrections, formatting, and minor rearranging of text should be flagged as a "minor edit". A major edit is basically something that makes the entry worth revisiting for somebody who wants to watch the article rather closely. So any "real" change, even if it is a single word, should be flagged as a "major edit".
The reason for not allowing a user who is not logged in to mark an edit as minor is that vandalism could then be marked as a minor edit, in which case it would stay unnoticed longer. This limitation is another reason to log in.
Credits: text taken from WikiMedia's help page. Visit there for even more editing help.