Quick Image Stabilization in After Effects

Step 1)
Import your footage into After Effects. For the purposes of this tutorial I'll be using footage found here, working from the shaky portion starting at the 2:22 point.

Step 2)
After making a new composition from your footage, make sure the Tracker is visible.
Activate it by going to Window - Tracker, and the panel should pop up in the bottom left corner.

Step 3)
Click the Stabilize Motion button, it'll throw a tracking point onto the screen.
Place that point on a portion on the screen that never leaves and Analyze Forward through the footage to get it to stick.You want something stationary to track, but for the shot I'm using there is almost nothing to latch onto. So I'm forced to use a light hit on the foreground character's nose (not pictured).
As the character himself moves around, this is far from ideal.
If the tracker slips off your designated point, you may have to go back to the frame that happens and adjust manually before continuing. 

 Step 4)
Hit the Apply button once your track is locked in and click OK when the window pops up to confirm which dimension you are applying the move to.

 Step 5)
You win! Enjoy your newly stabilized footage!