Hi, Kendall- You should probably wait until the printer stops doing what it's doing, and then turn off the computer and then the printer. Wait five minutes, and then turn on the printer first and then the computer.
Next time, remember not to touch your printer while it's working. You can sometimes cancel a printer's operations by clicking on the printer icon on your computer (or like Bert says, in the Control Panel), but it won't stop immediately. Yes, it's very much like the Sorcerer's Apprentice.
Your printer and monitor and most other equipment should be turned on BEFORE you turn your computer on, and should be turned off AFTER you turn the computer off. I just leave my printer turned on all the time, and that seems to work well for me.
-Joe Offer-