GENERAL CONSIDERATIONS:
The length of the approach shot has a lot to do with green size and shape. Beyond that, I'd have to think that the amount of play expected on a set of greens would influence the architect. (When Tour 18 in Texas built some smallish greens, like Augusta #12, they didn't realize that such a small green couldn't stand the traffic load they experienced during the course's early burst of popularity as an oddity. They had trouble keeping some of them alive through the summer)
SPECIFIC GREEN CONSIDERATIONS:
The architect's vision for the course difficulty,the strategic way to play each hole, and the number and variety of pin positions desired might be guides for shaping details into a green.
INTERESTING EXAMPLE:
Champions Golf Club, built by Ralph Plummer for two pretty fair country golfers, Jimmy Demaret and Jackie Burke,Jr. has huge greens averaging 10,000 sq. ft. This was partially required by the length of the course being par 71 and over 7,200 yds.
They created a lot of pin positions and variety in difficulty by designing lobes projecting out around the perimeters of some greens, protected by sand, grass traps or water. The centers of many greens are higher than the edges, allowing pins to be tucked into the hazard protected corners. The prudent shots to these pins is toward the centers of the greens which gives many downhill, scary putts out to the perimeter lobe pin positions.
This feature of the course allows them to make the pin positions as easy or challenging as desired.