Where do the mined bitcoins go?
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.