You installed the adb program correctly. The Android Debugging isn't activated by default. The activation option is hidden.
You'll have to reveal it with these steps:
Goto Settings -> About phone -> (scroll to) Build number ->
(Tap on it about 7 times) -> (You should get a notice
You have enabled the development settings)
Now you will have a new menu item in settings called Developer options.
Go into this option and turn on the USB debugging option.
Now when you plug in the USB cable to the computer, you will get the prompt to Authorize the connected computer.
After the debugging is turned on you may have to restart the server. You can do that with these commands:
#on your adb server
$ adb kill-server
$ adb start-server