Is it a slide switch or a push button?

With the slide switch type, the car will automatically shift into overdrive when you are in 4th gear - if the switch is in the "on" position.

If you have a push button, you can engage overdrive in 4th gear only (it is locked out in gears 1, 2 and 3 by means of a switch that senses when the transmission is in 4th) by disengaging the clutch, pushing the button on the shifter, and then releasing the clutch.

As to how it works. The transmission is a 4-speed gearbox. The overdrive is hitched to the rear of the transmission and is, essentially, an automatic gearbox with only one ratio. The switch is connected to a relay which in turn powers a solenoid mounted on the transmission. When the solenoid is actuated, transmission fluid flows past the piston in the solenoid and if it is at a high enough pressure (determined by road speed) the overdrive will engage.

It is called "overdrive" because the effective gear ratio with overdrive engaged is better than 1:1 (0.84:1 from memory). The output shaft is turning more than one complete revolution for each revolution of the input shaft, thus "overdriving" the transmission. The result is a lower engine speed, lower fuel consumption, and less engine noise on the highway.

A different means to the same end as a 5-speed stick