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.
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 cachetmaker's contest and an event cover column in its journal, First Days.