Today on how to shake your camera: Tripod Trick!
You will need a sturdy tripod with extendable column for this one. "Sturdy" means, the column should not easily be turned or shaken when unlocked. This shot is more difficult if your camera or tripod is lightweight, because heavy things are steadier due to their inertia.
Extend the column to some 30-50 centimeters and compose your shot. Use the self-timer or a cable release.
Hold the column with your hand near its base, unlock it and carefully let it slip downward. While the camera is slowly descending, make the exposure. Don´t start the exposure while the camera is still resting or there will be a still part in your image instead of a smooth blur. Expose for 1/1-1/15th of a second, depending on the light. The example shot was exposed with 1/10th of a second.
This technique gives beautiful exaggeration of vertical lines. Looks quite like a Feininger, doesn´t it? (I mean Lyonel, not Andreas). Of course, if your tripod is sturdy enough, you can also pan the camera for horizontal effects. Note that I didn´t align the camera exactly horizontally for my shot. The buildings are slightly tilted towards the middle of the frame. But the movement effect pretty much conceals this.
Some gifted humans might even be able to shoot this hand-held. I reckon that you´ll only get a real nice vertical blur if you move (not tilt) the camera vertically, because everything else includes too much lens distortion and nodal point problems (read: "thing move in weird ways if photographer moves camera in weird ways").