The objective of this game is to line up the red atoms with the hidden atoms only by matching their diffraction patterns. In order to get rid of a translation invariance problem, the red atom in the lower left corner is already correct. Don't move this atom. Or if you do put it back, or put another one in its place. You can always show the hidden atoms and line them up to see that indeed when the atoms are aligned the diffraction patterns match. But that's cheating.
To move an atom, highlight it by clicking on the red spot. You can then test other possible positions by clicking anywhere in the blue. Clicking on another red atom changes your selection. Arrow keys also move the test atom. When you enter a test atom, it appears as a white spot, and the new diffraction pattern appears alongside the old one. This would be the diffraction pattern with the "white" atom replacing the "orange" atom. Once you are happy with your atom's new position, click on "Accept". If you don't like it, click on "Reject". Until you click on either, you can change the test atom's position constantly. When you think you've got a good match, click on "Show"
My advice: Fix the central peaks first and then move your attention to the peaks further outward. The message box in the top left corner will given the cost function of the current diffraction pattern. The cost function is a summation of the positive differences between the diffraction pattern of the current atomic configuration (red atoms) and the diffraction pattern of the hidden black atoms. When the patterns match, the cost function is zero. Obviously, you're not going to get a perfect match. About as perfect as you can get is about 0.01. Therefore, if your cost function is not close to this number you're not done yet.