FIRST OF ALL I need to stress that transmissions are not something I would recommend a novice mechanic trying to tackle. Especially a Chrysler transmission.
There has been a number of TSBs about this problem. Unfortunately there has been no same answer for all of them.
I'm going to assume you have the 3.5L HO engine since it has been the most problematic.
First you need to check the fluid level in the transmission. In some of the vehicles you have to have a dip stick that you order FROM Diamler-Chrysler as they are not included with the vehicle. Once you have acquired the dipstick you have to let the car sit idle until it is at it's normal operational temperature which should be in the neighborhood of 212 degrees (give or take a little). Now you insert the dipstick into the refill tube and when you remove it there should be fluid up to the 60mm mark. Use caution when adding transmission fluid because it usually doesn't take much and it WILL SET OFF A CODE IF YOU ADD TOO MUCH. Not to mention there is no drain plug for the tranny to remove fluid. Also when checking the fluid check for signs of signs of water contamination (pink, foamy) or burnt clutch material (dark, smells strong). If there is water you need to break the transmission down, clean it out, and replace any damaged parts and all electronics that may have been exposed to the water. If it is a burnt clutch you simply need to replace the clutch (make a new bulletin if you need help with that as it can be a lengthy process and would take up a lot of room on here.) Another thing to check for is to place the vehicle on jack stands or a lift if you have one and have someone shift gears. Look for the shifter linkage to move. If it moves then you have an internal problem and you must tear the transmission down and visually inspect the internal parts. If it does not move you need to use a digital multimeter to see if the servo that controls the shifter linkage is working properly electronically. If the voltage seems okay and it was the servo not working then you need to remove the servo and try to operate it manually. If you can not then you will need to order a new one. Also, is the check engine/transmission light on? If so take your vehicle to an automotive shop or dealership and have it checked with STARscan or some other scan tool to identify the code that has been set. You can usually save yourself a lot of grief and time by doing this first. Make sure the technician that checks the codes tells you exactly what the code means or if possible print it out for you if you intend on tackling this problem yourself. Do not assume this is an easy task. Transmissions in today's vehicles are vastly more complex than an old turbo 350. Many chrysler vehicles use hydrostat transmissions with have literally over a thousand parts, nuts, bolts, sensors, and not to mention the electronic parts involved to operate them. So if you are not confident you can diagnose the problem by yourself it would be best to let the technicians handle it. And having it towed to the shop half way disassembled will only add time to the repairs that need to be made.