Former projectionist here, let me weigh in on what's happened in the last 7 to 8 years.
A bit of background: I started working projectors for my local theater in February 2007, and my last night was in March 2011. I no longer work this position because they transitioned to being completely digital, and I was among the first cut as I was only in one or two nights a week. Over the next 4 to 5 months the rest of the projection staff was gradually cut as the transition to 100% digital took place.
Alright, so now that we have that out of the way, I'll tell you what I know.
When I started, film was still distributed on 35mm reels. Depending on the company that pressed the movie to film, it would come in either a large, cardboard box, or several metal cans. The boxes could hold about 6 to 7 reels, the cans could hold about 3 reels.
Now, "Back in the day," my dad also worked projectors for a bit. This would be back in the 70s, and you would have two projectors for each theater. He'd load up reel one, start it, then he'd wait to see the cue mark, or "Cigarette burn," in the upper right corner, he'd start up reel two on the other projector, and when the second cue mark appeared, he'd cut over to this other projector. There's a reference to this in Fight Club, and it's completely legit. You can also see an example of this process in Inglorious Basterds, as Shoshana runs the Nazi propaganda film towards the end of the movie.
Flash forward about 35 years, and when I started working projectors you no longer had to do this. Cue marks would still appear in the upper right corner, but in the last 15 to 20 years of film still being on 35mm, things transitioned to what's called a platter system, which is why my theater used.
Here's what that looked like:
Rather than cut projectors between reels, we could now build the movie into one large reel to be fed through the projector. The film would "pay out" from one platter, and "rewind" on any empty platter. There were three platters so we could show two movies on one screen, though only one movie at a time, for example: a kid's movie during the day, and a R-rated film at night. Each week as movies would move to smaller and smaller screens in the building, we'd also have to move the prints from one projector to another. Some movies were so large they had to be broken down by a few reels, then put back together (Lord of the Rings for example). Each reel was about 15 to 20 minutes of film. We could easily tell each individual reel on the larger reels because they'd form a sort of tree ring pattern, making it easy to identify problems like, "There's a large scratch halfway through reel 4 that needs to be changed out."
How did we piece the movies together? Very clear tape. I'm not even kidding. Your entire movie was held together by tape. We'd use a special table to build the movies, that would pull the film off the reel and onto the platter. You'd put a small film ring in the middle for any pre-show ads and trailers, then would build the movie onto that (the small reel on the lowest platter in the picture above is what a trailer reel might look like, though a bit smaller in most cases). You'd start with reel one, and continue until you were finished.
Further, movies were either flat (1.85:1 aspect ratio), or scope (2.35:1 aspect ratio). Depending on the movie, we'd simply rotate the lenses in the projector, and slide a plate into place behind the lens to channel the bulb's light directly into the frame of the film. We'd then have to walk into the theater and adjust the masking to change it from 1.85 to 2.35 or back the other way, depending on the movie being shown.
All in all, the process could take a few hours. Busy summer weekends could take as many as 4 hours to build all the movies.
My theater also had rollers setup to allow us to "sync" single prints of a movie between two or more projectors. All the projectors were networked, and we could put them in sync groups so when the movie was started on the first projector in the group, it would start all the other projectors in the same group. We'd thread a single print through 2, 3, or even more projectors for midnight shows, or if demand for a movie was really high. This way we could show movies on more screens with fewer prints. One of my last summers there we ran all our projectors, over 15 in total, on 4 prints of the latest Harry Potter film. Set some sales records that night, and we bit our nails the whole time.
When a movie left the theater, we'd tear the movie back down to its individual reels, put them back in their respective box or can, and leave them at one of two areas of the theater (depending on the company that sent them) for some guy to pick up. They might go to a second run theater, they might go back to the studio.
Those days are long gone, though, and nearly everyone is using digital projectors now. The first projector our theater got was around the time Journey to the Center of the Earth came out, and was also our first 3D projector. We eventually added two more over the next 1.5 years, and finally the decision was made to go all digital. Early on, the movies would arrive on small hard drives and we'd load them onto the computer for each digital projector, and unlock it with a key on a USB drive sent with the film. Now they can load the movies onto a central server, and serve it up to each projector based on need, along with pre-show ads and trailers. Everything can be fully automated now. Digital projectors are also capable of showing movies in 4K resolution or higher. Contrary to popular belief, digital movies are NOT run off a DVD or Blu-ray, because the amount of data for a full resolution film with completely uncompressed audio is far too large to be held on a single disc.
Sorry if my answer is long winded, but it's a part of the industry I miss and could provide a good amount of detail on to really flesh out any questions you may have regarding the old way things were done. I'd be happy to flesh out any bits anyone has questions on, though I can't speak too much about the current state of digital, as it was, "After my time."