Ore is harvested with a Pickaxe, which you can't obtain until Campaign Day 2 at the earliest.
Once you have the pickaxe, look for harvestable rocks.
Walk up to one and choose the option to harvest it. Ore will probably be among the things that pop out (but there is some randomness involved).
- There are several different types of Ore. The one that pops out may not be the one you wanted.
- There are several qualities of rock, and several qualities of tool. 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.