Tools - Successfully complete the indicated task to get the corresponding tool:

Axe: Till 40 squares of land (you do not have to plant anything), and talk to Stella the nun (you may have to wait until Spring 4th).
Fishing Rod: Talk to Cinnamon by the church district exit on your farm in the early afternoon.
Hammer: Go to the second floor in the cave on Whale Island to find Melody. There will be a cutscene, and she will give you a hammer.
Harvester: Given to you by Candy. Ask her "What are Runeys?"
Hoe: Given to you by Mist when you first move in.
Pet Glove/Brush: Speak to Kross after exploring the cave on Whale Island a bit. He is found in the south district.
Sickle: Till 40 squares of land, and speak to Erik. He sells seeds in the south district.
Watering Can: Given to you by Mist when you first move in.

Cinnamon and Candy - Cinnamon and Candy are granddaughters of Kanno who will not arrive until Spring 7th. You must speak to him several days before they come to town. They all live in the clock tower.

Finding Woolys and Buffamoos - Enter Whale Cave, and make your way to the left whale wing.

Getting to Whale Island - Water the sparkling plant found near the clock tower.

Getting fruit from the fruit trees - Hit the tree with your hammer, and it will fall to the ground.