A redirect is a page that has no content, but automatically sends the user to a different page.
Making a redirect is easy: it begins with the text "#REDIRECT", followed by a space, and then a link to the destination page.
When to use redirects
In general, redirects are used to point alternate spellings, capitalizations, plurals, synonyms, abbreviations, and other likely alternate titles to the same page. For example, the Warhammer 40,000 page is the target of the following redirects: 41st millenium, Warhammer 40k, Warhammer 40K, 40k, WH40k, WH40K, Warhammer 40000, 41st millennium, 40K, and W40k.
For an example of more advanced usage of redirects, suppose you want to link the phrase "plasma cannon." It doesn't have a page of its own, and doesn't really have enough content to make a page of its own, but the Plasma article has a section about plasma cannons. You could use a piped link that points to the "Plasma Cannon" section of the Plasma article, like this: [[Plasma#Plasma Cannon|plasma cannon]]. But that link is case-sensitive, and it's cumbersome to type that out every time you want to link that phrase. So instead, we make (have already made, in fact) a redirect from "Plasma cannon" to "Plasma#Plasma Cannon". This has the additional advantage that, if the plasma cannon content gets moved, we only need to change the redirect (in fact, the redirect provides a convenient place to make the full article, and everything's already pointing to it -- although the "Plasma Cannon" redirect would have to be changed in this case), rather than search through and update every page that links to the Plasma article.
We do the same thing with our Tactics pages. Articles link to the generic "/Tactics/" article, which acts as a redirect to that army's tactics page for the current edition. Then, when a new edition rolls around, we make a new page for each army, update the redirects, and move on with our lives.
When not to use redirects
Hard to say. One issue with using redirects is that, if you edit a page that links to a redirect to another page, that edit will not show up in the "Related changes" page of the redirect's destination like it will if you use a piped link. On the other hand, who uses the "Related changes" function? Redirects still show up on the "What links here" pages, which are far more useful.
Much like piped links, redirects can be abused as "easter eggs", like redirecting "Worst role-playing game of all time" to FATAL. Redirects should not surprise the reader.
Redirects will only make one "jump", so if you have a redirect to a redirect (for example, if a page gets moved, leaving behind a redirect to its new title, and then moved again), a reader clicking on a link to the first will be dropped onto the second redirect, and not to the ultimate destination. This is not good. The Double Redirects page has a list of all redirects that lead to other redirects; they should be resolved. Similarly, there should be an actual page at the destination of a redirect. The Broken Redirects page has a list of all redirects that point to pages that do not exist. Either make the page that they point to (or give the redirect itself some content), correct the spelling of the link, or, if that destination page was deleted intentionally, mark the redirect itself with the delete template.