Lantern Garden is a light-placement puzzle, known elsewhere as Akari. Every open square in the garden must end up lit. Tap a square to place a lantern there; tap it again to take it away. A lantern lights its own square and shines outward along its row and its column until a wall or the edge of the garden stops the beam.
Two rules keep it honest. Lanterns may never shine on each other, so two lanterns can never sit in the same row or column with only open squares between them. And a wall with a number says exactly how many lanterns touch it on its four sides; diagonals do not count. Blank walls place no limit.
Worked example
Start with the numbered walls, because they are the most restrictive. A wall marked 0 means none of its four neighbours may hold a lantern, so switch to Mark mode and mark all four as empty. A wall marked 4 is the opposite: every one of its four neighbours must hold a lantern. A 3 in a corner, where only two neighbours exist, cannot happen, so a 2 in a corner forces both of its open neighbours.
Once those lanterns are down, follow their beams. Every square a beam crosses is lit and can no longer hold a lantern, because a lantern there would face the first one. That often leaves a dark square with only one place left from which light could reach it, and that place must take a lantern.
Strategy tips
Mark what you know is dark. Mark mode is for squares that cannot hold a lantern. Marking them early shrinks the search quickly.
Hunt for lonely squares. An unlit square hemmed in by walls may be reachable from only one or two places. If only one candidate is left, it is forced.
Use the counter. The line above the garden counts lit squares against the total, so you always know how much is left.
Hints teach before they reveal. You have three hints per garden. If a lantern is in the wrong place, a hint takes it away first; only on a clean board does it place a new one. A garden solved with no hints and no facing lanterns earns three stars.