Theres a couple of different ways that people use discord. I would say by far and away the most popular on PC is to install the discord program on your PC, and then use headphones for gaming. You can have the game audio and the chat audio from your team mates on discord through the same headset. Discord has a volume control so you can adjust it so that the volume is just nice - loud enough to hear your teammates, but not so loud as to drown out the game.
Others use it on their phone. This is most popular amongst console gamers who physically can't install it on their console. This can work in a number of different ways - have the audio output from your phone like you're talking on loud speaker, you could plug headphones into your phone and just have one ear in and use the other ear to listen to your TV / speakers or you could have a high quality headset that allows you to connect to your playstation or xbox via a wired connection to the controller, then connect to the phone via bluetooth. This has the same effect as PC where you have both sound sources (discord and your game) coming through your headphones at once.
The first option is by far the most popular option on PC as using the app with a headset just works so much better and is so much simpler.
