There are a few steps and potential gotchas in setting up application debugging on your local device.
Ensure your device is connected to your pc and the device is visible on the computer
Enable USB debugging in the developer console
When you plug the phone into the PC you have to accept the USB debugging to the connected device
Ensure you tick remember this device for convenience
In android studio try and run your device, you should see your device in the connected devices
After selecting to run your device you may be prompted to install a device driver, install this.
Success - You can now run your application on your local device from Android Studio