Ok - this is perhaps one of the two hardest points in the game (i won't spoil things by mentioning the other), as the random nature of the game means that you cannot follow a guide, and as a timed event, you have to try and do it quickly.
To explain the nature of the game, what you have to do is make sure you delete all the lights on the board. The problem is (and key to understanding how to do it) is that when you push a button, it alternates the on/off status of the button you pushed, PLUS all surrounding squares (excluding diagonal). So, for example, on the 2nd puzzle (line of lights) if there is just one light lit and you click on it, it goes out, but the lights to the left and right will come on.
My strategy was to work out what position you need to get to, to finish the puzzle and work towards that. The first puzzle is fairly easy - try to get the bottom 2 lights lit and then select the lowest light.
The second puzzle, try to manoevre the lights so you have the 2 lights together, either far right or left, then you can click on the end light to put them both out. Sometimes you get lucky and the starting position is the two end lights!
The third puzzle, try to work getting three lights in a corner (any corner). Using bottom right as an example, try and get it so the very corner one is lit, plus the one above, AND one to the left. Then you can click on the very corner to complete the puzzle. The other alternative is to get the very middle one lit, plus the lights directly above, below, left and right.
As this is a purely timed puzzle, personally, bearing in mind the above, I just clicked like mad, working lights round the board trying to get to any of these positions. Try never to click back on a square you just clicked on, as you just undo what you did, and you'll go nowhere - just keep clicking and moving the lights.
Oh and good luck. This is definately a trial and error, with a little bit of luck achievement!