With Ethereum's imminent/recent switch to Proof of Stake a.k.a. "The Merge", Ethereum Classic becomes the largest Proof of Work Smart Contract Platform and inherits many of the miners that previously mined Ethereum. As Ethereum Classic's hashing algorithm is almost identical to ETHash, so it supports the same hardware, and mining ETC should be as simple switching to a mining pool that supports ETC.
Ethereum Classic has a long term commitment to Proof of Work, a tried and true consensus mechanism that provides a solid foundation on which to Build Unstoppable Applications. This commitment is not out of happenstance, but as an intentional design choice over other mechanisms, such as Proof of Stake, that come with inherent security trade-offs.
Mining is one of the most important elements of any Proof of Work blockchain, as it provides security allows nodes to reach consensus about the state of the network. In exchange for providing this service, anyone in the world, without permission, can contribute hash power and be rewarded every block with ETC, based on the emission curve and transaction fees.
Below is a non-exhaustive collection of mining resources developed for Ethereum Classic. If you have questions about mining, there is an active Mining channel in the Ethereum Classic Discord.