When you set out on your adventure, you'll immediately see just how much work went into the visuals in this game.
Explore the map
As you collect each core, a red star shows up on the map indicating that the area is complete.
Build up the Bastion
With each core collected, you can add a new building to the Bastion. Now you'll have a convenient place to switch weapons, make upgrades, and perform other useful actions.
As you play, you'll find special items that you can use as upgrades for your weapons. You'll need to find (or build) a foundry to apply special items to your weapons.
Wait, how does it work?
The upgrade screen doesn't tell you how to upgrade your items, but I realized you need to double tap the button on the right to spend your in-game currency and apply the upgrade to your weapon.