The vacuum hooks up to the vacuum modulator. That is a round cylinder with a vacuum pipe sticking out of the end. It is located on the passanger side of the transmission, just forward of the pan and a little bit above it. You can reach it from underneath but you will need the car supported high enough to get underneath. The vacuum modulator doesn't need to be connected for the transmission to shift into gear.

With an automatic transmission, the engine couples power to the driveshaft through the torque converter. There is no direct mechanical connection like there is through a clutch. The power is transfered through the fluid in the torque converter. You can think of it as two fans facing each other. If you spin one fan, the other will spin from the energy coupled through the air movement. In the instance of a torque converter, power couples from one fan blade to the other through the fluid. So, if you don't have fluid in there, you can't get the car to move!

There is also a pump in the transmission. The pump provides hydraulic pressure to operate the clutch packs. Without enough fluid, the pump won't build pressure. The clutch packs won't engage.

The fluid level is pretty important for an automatic transmission. It's purpose is much more than just lubrication. Don't overfill or underfill.