Step 1: Step One - Analyzing the Video for Motion
From the Menu bar, select Stabilize Motion.
Step 2: Step Two - Waiting :(
Let it analyze in the background. Be patient, this will take time according to the length of your footage and the quality.
Step 3: Step Three - Stabilizing
Same as step two, this make take some time. Just sit tight and let After Effects do its thing.
Step 4: Step Four - Done!
Congratulations your old footage has been now replaced with the stabalized version. You can preview it by using RAM Preivew or undo the stabalization with Ctrl + Z