I am trying to understand how the mining process works. I haven't ever mined, so I would probably understand it if I mine (maybe using zcash or another crypto that is starting). I understand the overall how the process of mining works, but what happens with the coins that a miner earns? Like, if I am a miner and I earn some coins after resolving the problem, where do all the released coins go? Do they all go to the miner? If so, can the miners hoard all the coins for themselves and not share them the rest of the world?
When miners are trying to find a block, they are doing so for a specific set of transactions. This set of transactions includes a special transaction, the coinbase transaction. It's the first transaction in a block and collects the transaction fees and the block subsidy. The coinbase transaction's output sends the mining reward to an address specified by the miner.
This way, finding a valid block also ensures payment of the successful miner: the payout is part of that block. Once the block has matured by 100 other blocks being built on top of it, the block reward becomes spendable. What the miner then does with the block reward is their own choice.