Mining Ethereum Classic is almost identical to mining Ethereum, and supports the same hardware and mining software. If you are a recently evicted Ethereum miner, Ethereum Classic loves its miners and welcomes you, and you can start mining ETC using your existing hardware by simply switching to a mining pool that supports Ethereum Classic.
The ETC Mining algorithm is almost identical to Ethereum's ETHash, with a small upgrade that made it more miner friendly. In late 2020, during the Thanos upgrade, ETC implemented ECIP-1099, which tweaked the ETHash algorithm into what became known as ETCHash.
Basically, in 2020, Ethereum's DAG exceeded 4 GB, meaning that many GPUs with 4 GB of memory would be unable to continue mining ETH. In response, Ethereum Classic tweaked it's algorithm to ensure that cards with 4 GB would be able to continue mining ETC until approximately mid-2025.
There are two main types of hardware that can be used to profitably mine Ethereum Classic.
Generally, the best graphics cards to mine Ethereum Classic are the most power efficient cards with at least 4 GB of memory. Before picking a GPU, look for reviews specifically about mining ETCHash. You can search online for the "Best GPUs for mining Ethereum Classic in [current year]" for suggestions, and visit WhatToMine for more info.
ASICs, or Application Specific Integrated Circuits, are specially manufactured chips that are designed, as the name suggests, to mine just one specific algorithm. Originally, due to the memory-intense requirements of the DAG, ETHash was fairly resistant to ASICs, but with time, like all profitable algorithms, there was a big incentive to build ASICs for ETHash, which did come to market.
A range of ASIC miners Ethereum Classic are available and can be found by searching online for "ETHash ASIC Miners", and check the manufacturer's specification for whether it supports ETCHash.
For further help and guidance from other miners in the ETC community, you can reach out in the #mining channel on Discord.