The low speed fan is activated by the pressure in the high side of the a/c system reaching a set level. That doesn't happen immediately, but generally does occur after letting the car idle for a few minutes (depending upon cabin and ambient temperatures).
High speed fan is activated when engine coolant temp reaches 105. There are only two fans speeds. Well, I suppose if you count "off", there could be three.

The a/c is disengaged when engine coolant reaches 115ish.
Most likely the low speed resistor or wiring leads to it are burned out. The first step is a visual inspection - the resistor is located near the a/c receiver/dryer. Make sure it's present, not crispy, and all wiriing is attached. Step 2 is to probe it using an inexpensive DVM. Test resistance across the resistor. Then let the a/c run for a bit and test for voltage between the resistor and ground.
Later 124 chassis cars had a wiring change that reduced the wire diameter running from the fusebox to the resistor. As a result the wiring sometimes overheats and breaks away from the resistor. If this is the case, it should be obvious.
Power for the resistor comes from a relay in the fuse box. The relay is activated by a switch on the a/c dryer. If you open up the fuse box - completely remove the cover - you *may* be able to hear the relay click when low speed fan is activated.
It's a whole lot easier to troubleshoot this when you have the wiring diagram in front of you...