Always start by separating. Color from color, pattern from pattern, edge from middle.
It is cheating to start with pieces already together, so separate those manufacturing errors as well.
Always have more than one thing going at a time. Edges are great for starting, but when a lull comes, you'll want to have a patch of color to work on.
When choosing, look for big blocks of color, but not so big to be undistinguishable by shade. Save those for last, when shape of pieces is all you have to go on.
Turn them over and over. Run your hand through the box, uncovering useful pieces.
Eventually, turn them all over slowly and collect them in your hand. Visual memory will be tested.
When large blocks come together, make big moves.
Before you start, make sure you have the space to move large blocks, and space for the whole.
Make big connections and fill in the gaps. Look for tiny bits of color on corners and the final few edge pieces.
Once the edges have come together, start fitting in pieces already set aside as different. Only the same pieces will be left in the end.
When all else fails (particularly your eyes) separate the pieces by shape. How many innies? How many outies? Zero to four. Put them all facing the same direction.
Here your patience is tested, painstakingly testing each logical piece. Start with the single spaces, then with the mostly surrounded ones, Three innies or three outies are usually the easiest to find. Begin snapping them in faster and faster...until they're all snapped in.
Run your hand over the ridges and valleys of your work. Step back and appreciate the whole which matches the picture. Hopefully no holes remain unfilled.
Start loosening row by row and enjoying the cardboardy sound as large handfuls drop back into the box. This takes awhile if done properly, so that no connected pieces remain for the next time.
The next time rarely comes. New pictures begin. Start over by separating.