Tap the "New Game" button, which slides away to reveal a tray of targets beneath. If the "New Game" button isn't visible, it means that a game is in progress. You can tap the "Finished" button on the left to clear it out and start over.
Tap a ray bay (one of the 32 five-side red shapes around the outside) to fire a ray. In order to fire precisely the one you want, you can hold your finger down on the edge and an orange halo will appear around the ray that's going to fire when you release. You can slide your finger along the edge to position this halo, releasing on the ray bay you intended.
Place your guesses on the grid by tapping that cell to summon a target from the tray. You can drag placed targets. Dragging them off of the board returns them to the tray.
When you're satisfied with your guesses, tap the "Finished" button to reveal the targets' true locations, see the ray paths, and your final score.
Tap the "hamburger" menu in the upper left to open the settings menu. When a game is finished, you can change the settings for the next game.
Understanding Ray Paths
Rays travel in a straight line out of the bay, unless stopped, bounced, or returned by intervening targets. When the ray has finished its journey, the ray bay is covered with a marker indicating what happened:
The ray was stopped: like a stop sign, a red marker means that the ray hit a target head-on.
The ray was bounced: the ray passed within one cell of a target and bounced off its "corner". Rays always bounce at 90 degrees. Think of the target as being surrounded by a field of eight cells (something Obscurant encourages with its pulsing halos around the targets): the ray is bounced 90 degrees away from the target. Both the ray bay from which the ray was fired and the bay in which it ended are marked with matching symbols. The path is symmetric: if you had fired the ray from the end of the path, the result would have been the same, so matching markers are appropriate.
The ray was returned: a special case of bouncing where the ray returns to the very same bay from which it was fired. This can happen if the ray tries to pass between two targets separated by one cell, or when a target is on the edge of the board immediately to one side or the other of the ray bay.
This Wikipedia article has an excellent explanation with more detailed examples.
Lower scores are better: the object is to find the hidden targets with the least number of rays fired. Each marker that appears around the outside of the board adds one to the score. Thus, a ray stop and a ray return each add one, but a ray bounce requiring matching markers will add two.
When you are finished placing each of the targets in the tray where you believe they are, tap the "Finished" button in the lower left and red crosshairs will rotate in to indicate where the targets truly were hidden. Each missed target adds five points to your score.
Starting a game with the "show ray trails" handicap will double your score; seeing exactly where the rays travel is a significant assist.
Starting a game with the "keep targets off edge" handicap will also double your score. Using both handicaps will quadruple it.
You cannot change handicaps or the number of targets once a game is underway.