The sure way to find thr problem is by geting a multimeter($17 at walmart), and doing some essential electrician's job using the wiring diagrams for your car, whoch you can find at
http://www.autolib.diakom.ru:8001/CAR/BMW/1988/325i/WIRING DIAGRAMS/.
If one of the fog lights is still working that means that the relay is working, then the problem is from the fuse #29 till the plug. If the fuse is not blown then it's either the plug on the other end that is not giving a good connection, or the wire from the ground wire from the plug (the brown one) is not connected to the car's body properly. To check it just use the buzzer mod on the multimeter and check the resistance between the brown wire and the bear body( an unpainted screw going into body is good enough). If the resistance isn't small(should be around 0.2 Ohm) and the buzzer doesn't come on , then u need to fix that wire. If the fuse is blown and when u replace it it blows again, that means there is a short on the yellow-brown wire that goes from the fuse to the plug(the wire becomes balck near the plug). To check it
unplug the bulb and take the fuse off and measure the resistance between that wire and the body, they shouldn't be connected, so you shpould get infint resistance(the buzzer certainly shouldn't buzz). If it is shortened then you should visually trace the wire and find the place where it is connecting to the body and insulate that part. If it is not shortened then the only other thing is that the connection betwen the fog light relay is broken(simply check the voltage between the upper connector of the fuse and the body it should be 12 v, if there is no voltage then it's broken) or the wire that goes to your instrumental cluster is shortened, or there is a short in the instrumental cluster... Well I guess I am going to far, check the above mentioned and let us know what happened,
Good luck...