When a new block is found, the miner who finds it includes the 'coinbase' transaction awarding their own wallet with the block reward coins. The amount of coins rewarded varies depending on the crypto asset being mined, and the current distribution rate. At set blocks the amount of coins distributed is reduced by half, until eventually all of the coins are created.
Different methods of mining exist, but all serve the same purpose of securing the blockchain, confirming transactions, and introducing new coins into the system by incentivising miners. The most common method of mining is Proof of Work.