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Pretty much all settings already have very detailed information on the tool tips if you just hoover your mouse over them, so I'll just give a brief run down of how to set things.
Settings/Encoding:
Quality Balance - This is the overall image quality that OBS will try to stream, the higher the value the better, however if your bitrate isn't high enough to allow a stable stream you will get artifacting. This mostly affects streams with lots of motion, so if you are playing a slow game it's usually easier to get a stable stream at high quality.
Max bitrate / Buffer size - Max bitrate is the average bitrate that OBS will
try to stream at, depending on how demanding the scene is it CAN go over this. You should set it a bit below your max upload speed (even lower if you are playing online). Buffer size will render ahead of the stream so it can improve the quality when necessary. Setting this to the same setting as the max bitrate means that it will buffer ahead 1 second, x2 the max bitrate it will buffer ahead 2 seconds, etc.
Settings/Broadcast Settings:
These are all pretty self-explanatory
Settings/Video:
Base resolution - This will be your work scene resolution. Setting it to monitor is the same as setting your desktop resolution. You should set this to the resolution of the game you want to stream.
Resolution Downscale - This will do an hardware (GPU) scale of the scene before encoding and streaming. If for example you play at 1080p, but only want to stream at 720p because of poor upload speed this is where you should downscale.
Settings/Advanced:
x264 CPU Preset - This will define how fast the stream will be encoded, faster encoding means less CPU usage, but it will also mean worst quality. Usually a "veryfast" encoding will be good enough, but you can go slower if you have a powerful enough CPU.
Send Buffer Size - This setting will buffer any the stream (not the actual encode) before sending it, causing a delay on the stream, but helping you get a stable stream without any hiccups that might be caused by connection problems. It's recommended that you enable this even if you use the smallest amount of buffer size.
Setting up your stream work space:
Scenes - This is where you will manage your scenes. Right click to access the menu. To switch between scenes during a stream you simply left click the scene you want to switch to.
Sources - Each scene will have it's own setup of sources and this is where you set them. Right click here to access the menu and add new sources.
Software Capture will capture the desktop or a specific window in the desktop.
Video Capture Device will let you use an external source, like a capture card, or DXTORY.
Game Capture will capture the game directly, this is what you should use, however keep in mind that if you are running a 64Bit game you will need to run the 64Bit version of OBS. Also this isn't compatible with all games, but you can use DXTORY for games where it doesn't work.
Global Sources - This will let you configure a source that will be shared through any scene.
Dashboard - This will open a browser with whatever page you set up in the Settings.