After the introductory cutscene, the game begins with you having just arrived at the Ghostbusters' headquarters: the Firehouse. Egon is about to activate an experimental Proton Pack when Peter suggests you be the guinea pig. Just as you're fitted in, the massive psychokinetic shock wave seen in the intro passes through the firehouse, and the wave results in Slimer breaking free from his containment unit. Follow the guys down the fire pole and down to the basement. On your way there, find the water fountain and have a drink; this is the first of eight you can find to unlock an Achievement.
Once you're in the basement, you'll discover Slimer looking into the Containment Grid. Ray convinces you to have a shot at Slimer. Do so, but Slimer will move away at the last moment. Your shot will damage the Containment Grid and allow a Sloth Ghost to escape. It and Slimer escape to the sub-basement, and Ray calls for you to follow him down.
Once in the sub-basement, Ray will give you basic instructions on the Proton Pack's Health and Heat gauges and then talk you through your first ghost bust. Attack Slimer with your Blast Stream. Weaken him enough and he'll eventually flee, leaving you with the Sloth Ghost to bust. Attack the Sloth Ghost, and then you'll be instructed in to wrangle the ghost and finally to trap it.
If you feel brave, you can also wait and have Slimer or the Sloth Ghost charge and slime you, unlocking another Achievement.
Once the scene is completed, you'll find yourself next to Ecto-1. Interact with it to complete the stage.