For beginners
A first day cover is an envelope posted on the first day of issue of the stamps that are on it. So if you go to your post office on the first day that a new stamp (or set of stamps) is issued, stick it (or them) onto an envelope and post the envelope there and then, that will be a first day cover because the postmark will be the same as the issue date of the stamps.

For experts
GBCovers makes very small editions of Official First Day Covers. They all bear GB Commemorative stamps (not definitives except for a few rare exceptions). Our first day cover envelopes are hand made and they really are 'different', you'll love 'em or hate 'em. GBCovers is run single handed by Derek Williams. A retired octogenarian doing this for a hobby, living in London, England and selling to a small band of collectors in many countries.