Single field alternator is pretty simple. You put 12v on the field and the alternator puts out. If it doesn't then the alternator is kaput. You can run a jumper for a quick test and measure at the output stud on the alternator. If it put's out like that then you need to figure out where the 12V to the field terminal is being lost in the rest of the system. You see Oz's schematic, you gotta have 12V to the regulator, a good ground to the regulator and it's cycle 12V out to the alternator to turn it on and off (if it's the old mechanical type, the electronic versions are smoother).

Looking at your engine compartment pic, the regulator is that black box to the driver's side of the master cylinder. It should have 12 on the IGN terminal with the key in run. The FLD terminal is the one that goes to the alternator field, make sure someone didn't swap the wires around.