I have always printed, cut, and put pieces together myself up until I started doing freelance work. Since then, I have used Anderson Minuteman Press (Glen Burnie) for my school and freelance projects. However, for my '9-5er' we use a variety of printers (Schmitz, Pavsner, Minuteman, Tray [print broker], Head Graphics, Ironmark) based on the project type, turnaround time needed, and price. It's definitely been a learning curve in working with printers as opposed to doing it all myself, and I'm still learning. I revert back to Lynda.com a lot because it really is a great resource. They have quite a few videos on the print production process, including what to expect and do when attending a press check. I've attended a couple for our university magazine, and it is true that the first visit can be intimidating. But it is very cool to see printing process. I never even knew there were different printing techniques (offset vs. digital) until I started working as a full-time designer. I think that this essential information is unfortunately left out of a lot of design education so it's important to supplement. Lynda.com: Attending press checks
If you don't have a Lynda.com subscription, you can search around on YouTube for some corresponding videos that Lynda.com has made available through YouTube. Some videos are still available on Lynda.com for viewing without a subscription, but entire courses are for subscribers.