Troubleshooting vibrations in a 1996 Dodge Caravan isn't very different than doing the same for other minivans or front-drive cars of its caliber. The Dodge's simple front-drive layout means that it will manifest symptoms similar to those of other cars, and the optional all-wheel-drive system doesn't change that much. The key to finding the source of your vibration is to focus less on where it occurs than on when it occurs.
Vibrations at Idle
A vibration at idle, in park, can only be one of a few things. If the entire van shakes in park, then odds are best that you've either got a cylinder misfire -- indicated by a "check engine" light and engine codes P0300 through P0306 -- or a bad motor mount. The Caravan uses a transverse engine layout, so a bad motor mount will typically result in a back-and-forth vibration, as opposed to a side-to-side vibration. If you feel pulsation in the steering wheel while attempting to turn it, then you have a malfunction in the steering rack valving. Vibration in drive with your foot on the break generally indicates either a vacuum leak or a malfunction in the torque converter or converter lock-up mechanism.
Vibration Under Acceleration
A vibration that worsens when you accelerate but is not linear in severity to speed indicates either a malfunction in the driveline -- the transaxle or CV joints -- or a misfire resulting from either excess air, not enough fuel or a malfunction in the ignition system that only manifests when it's under stress. Causes of fuel starvation include a clogged fuel filter and malfunctioning fuel pump; excess air problems may result from a vacuum leak, or a dirty or malfunctioning mass airflow sensor. Either of these will trigger a "lean condition" trouble code and "check engine" light.
Vibration that worsens linearly to vehicle speed usually indicates some sort of cyclical vibration: Put simply, it means that one or more of your wheels are either bouncing up-and-down or are wobbling side-to-side. Lost wheel weights will throw the tire out of balance, and a bubble in the tire tread will bounce the tire every time it impacts the road. A suspension in need of alignment, or bad control arm bushings -- rubber isolators -- will allow the wheels to wobble back-and-forth. The same is true of bent, broken or worn steering components. Bad wheel bearings will also cause a vibration that increases with speed, but will also emit a tell-tale grumble or grinding noise.
Vibration Under Deceleration
Bad suspension alignment can manifest under braking, and worn or malfunctioning steering end links almost certainly will. This is especially true if you feel the vibration snaking its way up through the steering wheel and into your arms. Warped brake rotors may also cause front-end vibration, but you should notice a distinct pulsation in the brake pedal and likely the steering wheel. The same is true of a bad ABS modulator, which may malfunction in such a way as to cause pressure fluctuations in the brakes. If the vibration feels more like a jerking shudder than a true vibration, then you may have a problem with the transmission, torque converter or converter lock-up mechanism.
Vibration While Turning
Alignment problems, worn bushings, bad wheel bearings and worn or broken steering components may worsen in intensity while turning one direction or the other, but will likely vibrate at other times as well. If your vibration happens only when turning, it could indicate the initial stages of these failures, but it could just as easily mean that you've got a bad outer CV joint. Broken teeth on your differential's pinion or axle gears would also cause vibration while turning, but this is pretty unlikely given the Caravan's relative lack of low-end torque.