Get in the mine cart and go to the area of the mines with the one-way door. Pick up the nearby pickaxe. Go to the mine area labeled "Gold" by several signs. Ride through it until you stop in front of some gold. Use the pickaxe to get some of the gold. Leave the mines and go to the boat dock. Ride the boat to the stone bridge. Give the bridge the gold then cross it. You will see three tic-tac-toe boards on the other side (3x3, 5x5, and 7x7). Click on one of them to play a game of Cheese And Crackers, which is a tic-tac-toe type mini-game.
In Darkness' Kitchen, select either the pot on the stove or the cutting board (not the knife itself!) to make them sing. Alternate between the two. This trick may work best if one is selected immediately while the other is singing. Eventually, after a few verses of each of their songs, the dumbwaiter will add an extra verse, the pot will jump into his mouth, then leave and return.
Remove the rust from the mine cart. Go into the area that is labeled "Gold" by a group of arrows and signs. When you enter it, you must click the directions you want to go quickly. Take the left path, then the upper-left path, then finally the upper path. If done correctly, you will stop in front of an arcade machine that lets you play the Nuggets mini-game. In Nuggets, you will be in control of a mine cart and have to collect gems while avoiding various obstacles and picking up bonuses.