There's a series of levers around the outside of the tic-tac-toe board, separate from the lever that starts/stops the system, and the ones that select the mode. Initially the first one is pulled. Go pull the next one, and the golem should tell you that you're now on Rank 2.

Beware, though... at higher levels, some of the monsters can teleport, and this means that they have a tendency to teleport halfway across the map to where the rest of your party is placed while your chosen one fights the monster. When they do this, the golem will try to follow them, and has a tendency to get lost. If he gets lost, you usually either fail the square (even if you beat the monster) or the entire battle system gets broken, or both.

So always save before you click a square, and if your monster teleports away, reload.