Ore is harvested with a pickaxe which you can obtain from one of the bears early in the story.

Once you have a pickaxe, look for harvestable rocks. These rocks will have ore veins allowing you to easily distinguish if they are harvestable or not.

Walk up to a harvestable rock then click on it to start harvesting it. You may receive iron, silver, or even gold ore from a harvestable rock. However, keep in mind that there is some randomness involved. You may also receive other items such as skipping stones.

Notes:

• There are several different types of ore and it's not guaranteed that you'll receive the type you want.
• There are several qualities of rock and several qualities of tools. Your initial pickaxe will only be able to harvest the lowest-quality rocks, but eventually, you'll get better pickaxes that can harvest higher-quality rocks.
• Unlike trees and pets, rocks can be harvested even if they're uncolored.
• After harvesting a rock, its appearance will change and it won't be harvestable again for a while.