If only one side isn't working and is flashing fast, it's a bulb. If neither side is working first check the fuse located behind the glove box door on the left side behind the fuse box door. The door has a diagram showing which fuse is for what accessory.
If it's not a fuse you will have to drop the dash down from the glove box over to the ashtray. (It's not hard.) Then right above the fuse block follow the red wires to the relay block. Reach above and toward the back of the car and then feel downwards. The relays are installed so they are not visible. The owner's manual says you can "push the block up and off" and drop the whole block down for easier access. My relay was original and yellow. Replaced the wrong one first but when the emergency flashers quit working it was easy to figure out. I hope this saves someone the hours of frustration I went through thinking the relays were pushed in front to back or upwards and I could see them.
If neither of these is the problem you may have to replace the turn signal/wiper switch on the steering column. Again, not difficult, but expensive and aggravating. First you need a torx/star screwdriver because the holes for the screws underneath the bottom part of the cowling are too deep and narrow for a bit with a driver handle. Then you need a tamper-proof star bit because the screws holding the switch on have the pins in the middle (I replaced mine with phillips-head when I found this switch wasn't my problem).
If none of these are your problem you have a short and will have to do continuity checks on the wiring and someone else will have to help with that.
Could be the flasher unit.
There are two flashers, one for the hazards and one for the signals.
check your ground wire in the back
check the fuse first!
I replace my flasher fuse.Now they light up but won't blink.
replace turn signal flasher, hazard flasher is separate
The 1990 VW Jetta turn signals will not work when the ground wire is broken or corroded. The turn signals may need the lightbulb's replaced.
Most likely a bad turn signal flasher or blown fuse
have you tryed all the fuses then check if the bulbs are good
If the turn signal bulbs light but will not flash, the flasher relay is defective, replace it.
Replace the starter motor
replace flaser can in fuse box