To start with you'll need the Android SDK to get started: http://developer.android.com/sdk/index.html but select for existing IDE so you get the tools rather than all of Android Studio.
In Chrome Beta on your Android device do the following:
Menu → Settings → Developer Tools → Enable USB Debugging
Hit the home key on the device and go to Settings → Developer Options → Enable USB Debugging.
(Note: If you can't see Developer Options, go to Settings → About Device. Then tap the Build Number a number of times and eventually you'll see a message saying you are now a developer or something similar.)
Connect your phone to your computer via USB.
On your desktop, open Chrome Canary (I think stable and Beta currently have issues):
In the address bar type: chrome://flags and enable - "Enable Developer Tools experiments" and hit the Relaunch button that appears.
Once it's relaunched open a terminal and run adb devices
. You should now see your device appear in the list. When it has, in Canary go to chrome://inspect there you will see your device, so now click inspect.
This will open up devtools for your Chrome on Android.
Now click on the cog in the corner, then go to Experiments → Enable Port Forwarding (if you don't see port forwarding, you might not be in Chrome Beta).
Once port forwarding is enabled, close and open dev tools.
Go back to the cog and select Port Forwarding. Then type in the port you want to forward (i.e., for localhost:9000
on my local machine I'd type 9000 [Device port] and 127.0.0.1:9000 [Target]
There is a bug open where the first port is ignored, so it might be worth hitting enter on the first line and re-entering the same details on the second line.
You can now put localhost:9000 (or your port number) in Chrome for Android and view the site and use DevTools to inspect the page.
More details are under Reverse Port Forwarding section of this site: https://developers.google.com/chrome-developer-tools/docs/remote-debugging