Starting from the second mine, you encounter abandoned buildings at the cave's sides. Those are very important! You'll obtain a new source of income when they are repaired. To repair the shaft, clear the boulders nearby and bring one of your goblins to its edge. Similar to rocks, you'll see a timer and circle bar indicating how long it would take to fix the building. Tap Activate when the repair is complete.
When the shaft is repaired, it starts generating gold similar to forge. Each shaft is quarrying one exact type of jewel. Jewels have different values, but that doesn't mean one jewel will always generate more gold than the other! Shafts vary by speed, upgrading cost, and the profit multiplier on each level. So while one jewel might generate significant profit at the lower levels, another might become way more profitable further in the game.
To upgrade your Mineshaft and increase its profit, press the green button at the bottom of the shaft. (if the button is grey, you don't have enough coins right now).
Similar to forge, you can see a spinning yellow bar, indicating the shaft's work cycle, but unlike forge, it doesn't send gold directly to your treasury at the beginning. You have to gather carts with gold manually, so pay attention to the progress wheel and grab the cart when it arrives!
Of course, it's quite tiresome to collect carts manually. You're the boss here - this type of labor is not for your level of competence. That's why you can automate the process by hiring a Manager to unload carts in your stead. To do that, you need to increase your understanding of the jewel using the jewel research cards (goblin managers are not very bright, they need a detailed manual on operating the shaft). Tap the recursion button at the side of the shaft to see the requirements for hiring a manager. That would be the type of cards you need (common or uncommon), and the level of research required. Even if you don't have enough cards to hire a manager, you can level up the jewel to increase its profit.
Remember: you need to activate every shaft in the mine to complete the level!