The design (called a "cachet") is generally placed on the left side of the envelope (although there are also "all over" cachets). It explains what is being commemorated on what date, and generally also includes an illustration page.
Ideally, the stamps used relate to the celebration (for instance, space stamps for a shuttle launch). Cancels are either obtained in the city of the event (such as Kitty Hawk for the Wright Brothers first flight anniversary) or, for larger quantities of envelopes, from a special cancellation unit maintained by the Postal Service in Kansas City, Missouri. If a special cancellation (one with a design) has been created for the event, you can generally only receive that cancel from the local post office.
A good example of a special Event cover was one by the Isle of Man Philatelic Bureau that was issued in 1985 to mark the anniversary of the aircraft Douglas DC-3, which was of interest, not only because of the high volume of air mail handled by Dakotas at that time, but also the link between the names of Douglas, Isle of Man, and Dakota - Douglas DC3. A 26p stamp was specially issued by the Isle of Man and a special handstamp was also created for these covers, which was deliberately created with a Dakota flying "free" and not boxed in. The envelope was also officially acknowledged by the McDonnell Douglas company and bore their official DC3 logo in the bottom right of the Envelope.
The earliest recognized event covers were presidential inauguration covers, which were first created in the early part of the 20th century (the stamp hobby calls envelopes "covers" because letters were originally simply wrapped in a blank piece of paper, or "cover"). Event cover creation and collecting is considered part of the first day cover hobby, which creates decorated covers to commemorate the issuance of stamps. Both fields are recognized by the principal cover collecting organization, the American First Day Cover Society, which includes an event cover category in its annual cachet-maker's contest and an event cover column in its journal, First Days.
Event covers can include mail that was aboard aircraft that flew the mail between two points, usually large cities, for the first time, however these covers are usually referred to as First Flight covers by collectors.