It looks like the transformer is the thing on the bottom, with the red and yellow wires attached. You'll need a multi-meter to verify this as you go - I wouldn't make any assumptions here, especially since it's older. Mis-wiring could cause something to break, and there's a chance finding a replacement will be very difficult.
Use a multimeter (on the "VAC" setting), and you should be able to measure 24V AC across the red and yellow wires whether the furnace is on or not.
Next, you need to figure out which power wire (red or yellow) is already going to the thermostat. Turn the furnace power off (you should now measure 0V AC on the red/yellow wires) AND the thermostat itself off, and use the resistance meter (Ω) on your multimeter to figure out which one of the red or yellow wires goes to the thermostat. You should measure 0Ω (or <1Ω anyway) between one of the wires of the thermostat and either red or yellow. Test both thermostat wires against both. The others will be infinite (not connected). If it's red, then the yellow is your "C" wire, or vice-versa.