“Will I be hooked up to a machine during my sleep study?”

I assume here that you are referring to an in lab sleep study. There will be electrodes (wires) attached to head and chest and legs. A breathing sensor will be placed near the nose and mouth. Most people have no particular trouble sleeping even in the odd environment that the monitoring leads cause. Also, every sleep lab has a low light camera to see what is going on during sleep. You are sleeping in a monitored environment, so don't do anything you would not want recorded.