Exit the Lumbridge Castle, and follow the path leading north. If you don't already have a bucket in your inventory, head over to the general store, located along this path, and purchase a bucket for a mere two coins. Continue following the northern path, heading around a large sheep pen, past the cabbage field, untill you reach a fork in the road. From here, you'll notice a small wheat field to the side of the main road. Head inside, and grab one bunch of wheats.

Exit the wheat field and the northern path. You'll arrive at a windmill. Make your way to the top floor of the windmill. Use the grain with the hopper, then operate the hopper controls. Now, go back to the bottom floor. Use your empty pot with the flour bin to to get your pot of flour.

Exit the cow pen and continue along the northern path. Shortly, you should come across a small chicken coop. Head inside, and grab one of the eggs that you can find scattered around the coop. If you don't see any, wait for one to appear.