ETC and ETH are technically compatible blockchains allowing applications to be deployed on either or platforms. You can use the same tools provided by either ecosystem in your DApp development environment. For example, Truffle and Remix can be used and configured to connect to ETC.
If you have an existing application on ETH, then it is often as easy as deploying that application on ETC and ensuring the interface is connected to the correct network (ETC). If your application contains a lot of infrastructure off-chain, then the scope of work could be more complicated, but if you’ve integrated ETH, then you’ve technically done it before.