This page contains a list of services that allow you to purchase or trade ETC.
The following exchanges all support Ethereum Classic. They are separated into 3 categories; centralized, trust minimizing, and instant.
Please do your own research on the exchange you choose to source Ethereum Classic. Being listed on this site does not constitute an endorsement of the exchange's services by the Ethereum Classic project.
Decentralization is a spectrum, and whilst the following "DEXs" are not necessary fully decentralized exchanges, they are designed to requires less custodial risk than the above.
Note: Instant Exchanges typically offer worse rates than Centralized Exchanges.