All you need to know is described on this page: Remote Debugging on Android with Chrome.
I tried to set up remote debugging on my Samsung Galaxy SIII. My operating system is Windows 7. My desktop Chrome browser didn’t discover my device.
I encountered one big problem in the step: “Discovering devices in Chrome”. In “Troubleshooting” part they suggest to install OEM USB Drivers on the Android Developers’ site. And I did everything what they said…. But my desktop Chrome browser didn’t discover my poor Android.
So, in conclusion, make sure to install Samsung Android USB Driver for Windows.