If you want to stream, you can just connect your PC or console to the internet and press a button or two. There's plenty of tools that will let you do that. But if you want a proper setup, things are a little more complicated.
The diagram was uploaded this morning by Twitch streamer AnneMunition, outlining the dual PC, triple monitor setup that she uses on a daily basis.
To capture footage from consoles, AnneMunition uses an Elgato HD60 Pro capture card for 1080p footage and a Magewell Pro capture card for 4K. Both consoles are plugged into a Zettaguard 4x1 4K HDMI switcher, with the output from that being fed into a 4K splitter and isolater. The audio feeds from the isolater than goes through to a Mackie 802VL24 mixer, while two other isolaters feed audio from the main streaming PC (which is equipped with a dedicated ASUS Xonar Essence STX sound card) into separate channels on the mixer.
The microphone and headphones are plugged into the mixer separately, with the headphones going through a Behringer HA400 amplifier. A line out from the gaming PC sends audio to another channel on the mixer, and AnneMunition uses the AUX Send software to transmit her microphone audio to voice apps like Discord. And if that wasn't enough, there's also separate hum destroyers and a compressor that jointly plugs into the first channel in the mixer.
So if it wasn't patently obvious: anyone can stream, but good streaming - not just having good internet, but maintaining a high quality stream - isn't easy. There's a lot of equipment behind the veil and a lot of pieces of software that could go wrong, especially if you want to cover all games and all platforms.