Theres umm, 5 wires on the metal relay, from memory, orange or red (depending on car), blue, purple, brown and black. Orange is the high speed power supply, some cars from the fusebox, others from a fuse link at the starter. Purply goes to the blower. Brown is the 12v feed from the dash switch on high, black is the relays coil ground. On the first 2 speeds, power comes from the dash switch, thru the resistor (depending which speed dictated which resistor) thru the blue wire, thru the normally closed contacts of the relay to the purple wire, giving you 3 speeds. On high, the brown should go to 12v which closes the relay and now the orange (or red) wire gets connected to the purple wire going to the blower, giving you high speed.
Since you have 3 speeds, go out to the relay, and with a helper have them flick the switch from med to high. You should hear/feel the relay click. If it does not, check the brown wire for 12v at high position. If not, check the dash switch for burned contacts (very common), if the relay clicks, check the orange (or red) wire for 12v, and if you have 12v there, throw a new relay at it as the contacts inside are most likely charred from arcing. The relay is kinda behind the accumulator, under the high side AC line orifice tube joint if memory serves me. Kinda between the AC line and the blower case.