I know very little about your car, but you will need a workshop manual, or at least the ABS system diagnostics section.
I went through this with my 1990 Volvo wagon, when I bought it, the ABS warning light had been removed from the dash, only found out about it when the rear locked up one day....
But I digress. On some vehicles around this age, the ABS system is linked into the self diagnostics system of the vehicle, meaning you can pull codes out of the system. You will need the manual for this.
On other cars, it's much harder. On my Volvo, I had to run through a long battery of tests, starting with measuring resistances and voltages at the ABS computer main harness connection, through to bridging certain wires to ground or +12v, to activate certain parts of the system. In the end it turned out to be a bad relay on the ABS pump.
The big bonus with ABS systems is that they are a very specialised system, so only one or two companies manufacture the systems and car manufacturers buy the system they want and have it calibrated to a particular model line, which means once you know a particular system you know most cars of that era. It also means parts are usually cheap to source too, if you buy from less "prestige" parts houses.
The really good news is that ABS systems are built to a standard, not a price, so USUALLY, the very large, expensive stuff like the actual ABS computer and pump don't fail. Most of the time it's a sensor or a voltage /ground problem.
So, get the manual and see how you go. No offence to anyone, but when I was trying to diagnose the issue on the Volvo, all I got was the old internet folklore " oh, it's the xyz, they always fail". And of course, it never was the xyz and when you read the workshop manual, xyz is never the primary cause in the first place!
What I found interesting is that about 85% of the potential problems listed in the Volvo ABS system are ground/power issues.
Just found this, it may help:
http://www.alfabb.com/bb/forums/164-168-1991-1995/160782-1995-164ls-ecm-abs-srs-diagnostic-connectors.html Regards, Andrew.