There are not so many places where a transmission can leak its oil.
- a sealing between transmission and motor #016 311 113B --> oil should leak between motor and gearbox. The gearbox must be removed. It would make sense to also replace the clutch as it is accessible then
- 2 sealings for the drive shafts #016 409 399B - you should see the oil coming from out of the inner side of an axle. Should be able to be replaced when the gearbox is mounted but that is due to be checked in the repair guide
- an axial seal #012 301 457C in the back of the gearbox
- the flexible sealing between the two housing parts of teh gearbox --> needs disassembling of the gearbox. The sealing is a liquid from a tube and must be applied manually.
- the oil drain plug on the bottom
Thanks for your excellent advice. When I get back I will get under the car and use your bulllet points to try to identify the cause.
I cannot recommend the idea of your workshop to just drive and refill. This does no good for your transmission in the long term. You really should either find another workshop willing to do classical repair jobs or maybe a friend who can help you with the repair. Replacing the gearbox with one from a crapyard is a gamble - you do not know how good the gearbox is and how it had been treated before.
Thanks for letting me know about this. For me the workshops advice sounds like something you give to a car you will only keep until the next thing breaks. I want to keep my Audi 80 as long as I can. My grandfather bought it in 1988 and nowadays you dont see that many on the road. They used to be common in Sweden but now even Volvo 740/940 are becoming quite rare.. 
All # are the Audi original part nos. referring to an 1988 Audi 80. You can find matching parts from other vendors online. I strongly recommend to purchase the repair guide for the car, especially the gearbox part. You can get it e.g. from VW/Audi out of the ERWIN system for a small price, or you try to find the printed "repair guide" which should be available for your car.
If you are out of transmission fluid your gearbox will die rather quickly. The moving parts and bearings need constant lubrication, otherwise they will weld together or break apart. Also there are plastic parts in your gearbox. Those will most likely melt.
First of all, are we talking about a manual or automatic transmission? If manual; 5 or 4 gear, if automatic; with or without sport-shift option?
First of all try to locate where the oil comes from. Try to get under your car, clean underside of the gearbox and then check from which direction the oil comes from.
Its a 5 speed manual transmission. 90 horse power engine. When I get back I will get under the car and have a look. Thanks!
