Just returned from Ks visiting Mom and Dad. Now one of the traditions is working on a jigsaw puzzle with Mom. We completed a 500 piece landscape scene and graduated to a 750 piece animal scene (a grizzly bear among the springtime flowers).
It seems a common methodology in puzzle construction is to begin with the border pieces followed by objects and the unique color patterns. Some people are more shape oriented while others look for color and/or unique image detail connections. I tend to sort pieces into common color groups keeping all pieces on the exterior of the borders only allowing pieces inside for those I'm specifically working on. I only sort by shape as a last resort.
The world's largest commercially-available jigsaw puzzle was released by German company Ravensburger in September 2010. It shows 32 works by American artist Keith Haring and has 32,256 pieces, measuring 544 cm by 192 cm when assembled. If it takes one minute per piece to construct you would work over 67 eight hour days to complete.
For puzzles in that category the best methodology to use is to find a puzzle partner or partners.
P.S. Here's a couple that put together an 18K+ piece puzzle in 2005 - http://chrisandnaomi.hathawayhome.net/news/family/the_worlds_largest_jigsaw_puzzle
or the Worlds Largest Puzzle contest in 2007 -24K piece
AND ---- The largest mentioned above http://slaterpuzzles.blogspot.com/2011/06/section-of-32000-piece-puzzle-double.html