first thing I do is hit the arrange button on the bottom and then the ghost button. (I discovered both those about 1 week into doing the puzzles.) However they're just a guide. I start with the edges, but as I go if I see pieces that will fit on the edges or to each other, I'll start that too. I leave the hardest to last and do the obvious ones first. I also don't worry at first where the inside pieces go and instead will build them outside the edges.

I think the biggest thing is learning to see subtle color variations. I actually tell my students that a good way to learn to visually see is to do jigsaw puzzles because you need to see very subtle variations in shade and color.

(It helped that today I knew the painting they have posted. <img border="0" alt="[naughty]" title="" src="graemlins/naughty.gif" /> )

Hope that helps.