I first sort out all the edge pieces and make the whole edge. Next, I just rummage through the box looking for starting points. Gradually group similar colours, look for distinctive features. When the easier parts are done, looking at smaller and smaller detail. For large areas of a similar colour, I might line up the pieces in neat rows, sorted by shape.
Here's a progress picture of a 3000 piece jigsaw:
Started with the edge. Then the purple bird and pink flamingo. The sky, zebra's, etc.. There is order in the chaos of pieces on the left. They are grouped by colour.
Last bit of that one, were the elephants. I ended up with a few hunderd grey pieces, but managed to put them together.
End result:
I recently got some sorting trays. This is the one I'm currently working on:
Good lighting is very important. And that's about all the "strategy" I got I'm afraid.
Hope you enjoy yourself! Maybe you can share some jigsaws here, if you're comfortable with that. Have fun :)