The easiest way to bridge your Matrix community with you Discord one is to rely on the free Discord bridge provided by t2bot.io.
It contains all the instructions about how to bridge your Discord channels with your Matrix rooms. Please refer to their documentation directly.
Here you can see a bridged room from the Matrix and the Discord perspective.
If you're interested in self-hosting your bridge or discovering all the Discord bridge implementations, please head to the Ecosystem > Bridges section of this website.