The SM 319 is a variant of the SM 318 3 speed that is standard in the '55-'66 trucks. Both transmissions also saw use in GM passenger cars in the same time period. The SM 319 is setup with a Borg-Warner overdrive unit in place of the tailshaft and its housing.
The main part of the transmission is the same as the standard 3 speed, so the shifter hookup and operation is identical. The overdrive is, if installed as the factory did it, shifted electrically via a solenoid on the housing. The shifting is done automatically by lifting off the throttle at approximately 28 mph (that speed can vary depending on rear ratio and tire size), which is when the contacts in the governor close. Overdrive can be used in any forward gear. There is also a manual lockout cable which locks the overdrive, making the transmission operate as a normal 3 speed.
If you use a transmission from a '55/56/57 Chevrolet Passenger car or '55-'59 Truck, no driveshaft mods will be required. The only change, depending on what the trans came from, would be to swap the shift cover out as Passenger and '55 6 cylinder Truck versions are different from '55-'59 Truck.
Here's the shop manual section from the '55 manual can explain things a little better on operation
http://chevy.oldcarmanualproject.com/shop/1955truck2/55ctsm0715.htmI've had one in mine for the last 20 years, it's probably the best thing I did to it.
