The Volkswagen Jetta has come with dozens of different engines and transmissions over the years. Diagnostic procedures when your Jetta won't shift out of Park vary from model to model, but a few basics apply to most of them. Some procedures rely on the car having government-mandated equipment like a reverse lock-out, while others will work only with Jettas of certain years and drivetrain configurations. Just take your time--there are only a few things that can cause this problem.
Check the reverse lockout button on the shifter. The reverse-lockout mechanism prevents accidental reverse/park engagement by forcing the driver to depress a button in order to engage those gears. The spring-loaded button pushes a small "dead-bolt" out of a locking hole in the shifter base. If the button will not depress or the shifter refuses to budge, the odds are that you have a malfunction in the reverse lockout mechanism. If you don't have a repair guide and don't want to take it apart to fix it yourself, any shop with import-auto experience should be able to help.
Inspect the shift linkage under the Jetta's hood for missing, bent or broken components. Aside from the reverse lockout mechanism, a malfunctioning shifter mechanism is one of the few things that will physically lock the shifter into park. If your Jetta uses a hard linkage (one that uses levers and rods instead of a cable), check the articulation joints for worn bushings, bearings or holes that will cause the pivots to go cockeyed and lock the mechanism together. If it uses a cable linkage, check to ensure that the cable-to-body, cable-to-shifter and cable-to transmission brackets aren't loose and flopping around.
Crawl under the Jetta and inspect the shift lever on the transmission itself. Lever locations vary by model year; follow the shifter linkage from the firewall to where it connects to the shift lever on the transmission. If the lever moves but the transmission won't shift out of park, then your problem is inside the transmission itself. At this point, you'll want to get some professional help from a transmission shop to further troubleshoot and repair the transmission. A general repair garage probably won't have the equipment to diagnose the transmission internals.
Have the Jetta towed to a transmission shop to have the transmission checked for internal damage related to the first and reverse gear fluid passages/servos/actuators. Almost all automatic transmissions go into park by engaging the first and reverse gears at the same time. A failure in either of these circuits can cause failure of parking gear engagement or disengagement. Possible causes of failure include blocked fluid passages, broken or worn modulator springs, and broken gear-sets and transmission input/output shafts. Electronic transmissions use a computer to engage the first/reverse gear servos, so the problem may also lay in a malfunctioning transmission control computer.
