Maybe the obvious answer would be, "Uh, take your camera off the tripod and shake it around," but using a "shaky cam" technique isn't as simple and straightforward as just shaking your camera around. In fact, it takes quite a bit of planning and choreography to really pull it off well in terms of focus, framing, etc.
So, if you want to play it safe and shoot from a tripod, this tutorial from Sam and Niko shows you how to quickly and easily add realistic looking camera shake in After Effects by adding null objects that simulate random movement from your wrists, arms, and body.
There are a few other methods for creating this effect, one of which uses the tracking data from your footage (which is then pasted into your footage position data), resulting in the movements your body naturally makes, but this takes a bit more time and energy to pull off. Using Sam and Niko's null objects method is a super simple and quick way to add the shaky cam effect to your project, though they suggest only using it on very short clips -- more than 2 seconds and your clip starts to look computer generated (because it is).
Source: Sam & Niko