Here is how I currently stream using just a single monitor with being able to see chat, webpages and other things at the same time without effecting the game capture.
First off the monitor needs to have dual inputs, the one I'm currently using has 3 different inputs: VGA, DVI and HDMI.
Next your video card has to support the two different types of input.
I'm using a 1080 GTX, it supports both DVI and HDMI.
I plug in both of the different types of connectors to the monitor. The monitor can switch screens between DVI or HDMI. For my setup I use DVI at 1920 x 1200 native, the max supported resolution for this monitor (its a couple years old) and HDMI at 1920 x 1080.
Since both DVI and HDMI connections are plugged into the video card, it will show the system as having 2 monitors.
I made monitor #2 as default (make this my main display) and monitor #1 is where all the games go for screen capture.
Here is how the desktop looks with the game running, OBS and a webpage with the twitch chat viewing.
Basically you put the game on monitor #1 which is really a ghost screen (not there) and then you use the OBS monitor window to play the game while its on the ghost monitor. And since its in a window you can load up webpages and other apps to monitor chat and whatever else you like during your streaming sessions.
Using only 1 monitor, saves power, creates less heat and doesn't strain your head and/or neck muscles as much since you dont have to keep checking to the sides if you were using a multi monitor setup.
