The Eagle (left) and Ralph McQuarrie's original concept painting (right)
Most of the time you see it in the film, the Falcon is a model and several were made for the production - the smallest being the size of a silver dollar - with the key one over 5 feet long (which was detailed with parts ‘kit-bashed’ from existing commercial models).
Modelmaker Lorne Peterson builds the core of the 5ft model, prior to kit-bashing and detailing.
There was also a full-size version built except that, in reality, only the starboard half of the ship existed. Reports vary as to why this was, though it seems likely that the partial construction was due to space limitations at Elstree Studios and also financial considerations (“A New Hope” went considerably over budget).
The original "Jabba" sequence, on Docking Bay 94 (a great behind-the-scenes shot showing the height of the partial mock-up. Note Peter Mayhew with his mask off, as Harrison Ford and Declan Mulholland (the pre-CGI Jabba) rehearse)
Seeing the Falcon for the first time, on the Docking Bay 94 set
After filming finished on the Docking Bay 94 set, it was transformed into the Death Star Docking Bay 327, since the set of the Millennium Falcon did not fit out the stage doors. Since this location was shown in wide shots, the Falcon was completed by a Harrison Ellenshaw matte painting.
Docking Bay 327, as seen in the finished film
Harrison Ellenshaw with his matte painting of Docking Bay 327 (the masked out area will be filled with the live action shoot later).
Putting the Falcon in place on stage.
Preparing to shoot