Not computers, for obvious reasons.
The two basic methods would be actually printing the words onto plastic sheets and rolling them through two drums, like unfurling a scroll. For example, this the classic Star Wars opening credit scroll. They’d just record the camera with a background (a sheet with holes poked into for stars) and slowly scroll the plastic film in front of the camera. Same thing for film credits.
For the graphics like, just words at the bottom of the screen saying a date or location, they could do the same thing but most likely did a double exposure. They’d film the scene normally, and then separately film just the words over a clear background and then create a composite after the fact. This was a very popular technique with regular photograph technology so readily reproduceable in the early film era as well.
No computers. Just text filmed direct onto film, then edited into the movie as needed. A variety of methods could be used to produce the text.
There are a number of old-school effects covered on the youtube channel corridor-crew. Highly recommend checking some of them out. I couldn’t find the episode quick, but one in particular covers a lot of old-school effects in some really old movies. But they often randomly touch on various techniques.
A lot of ingenuity, and a lot of work.
For some things they can use layers. For example, if a film wants to have a giant castle on a hilltop in the distance, they could paint the castle onto a glass slide and put that right in front of the camera, and then it will look like it is in the background. TVTropes provides [this example](https://static.tvtropes.org/pmwiki/pub/images/tmwwbk_3974.jpg) from The Man Who Would be King in 1975. The actors are filmed on a set or on location, and the painting (at the top) is put over them, and provided it is done well you cannot see the joins. [Here is another example](https://www.thepropgallery.com/media/wysiwyg/glassshot2.jpg) where you can see it being done.
Of course that doesn’t work if the filmed material needs to go in front of the image. For that you add in rotoscoping. A rotoscope is a device [that projects a film onto a painting canvas](https://en.wikipedia.org/wiki/File:US_patent_1242674_figure_3.png), so an artist can paint on it frame by frame. They could go through the film frame by frame and paint over the parts that need to be changed. Part of the point of using a bluescreen is to make this easier – making it really clear to the artist which bits need to be painted over or out.
Compositing was also a thing, whereby if a shot had multiple elements filmed separately (like a main part, a backdrop, a bit in the background) they would be filmed separately, and then the footage would be projected onto a screen with everything else blacked out, and then that would be filmed again. The film wouldn’t pick up the blacked out parts, so wouldn’t develop, and then you’d switch out what you were projecting and film it again, now only exposing the next bits.
Multiple-exposures (where you run your film through the camera several times, exposing different parts each time to layer on effects) can create very complex shots, combining many layers together, but can cause problems with the footage looking a bit washed out.
There’s a great documentary about the early work of ILM somewhere, but I can’t find it. However you might find [this video](https://www.youtube.com/watch?v=jAtULl3ExUo) on the making of the original Star Wars interesting. Star Wars pioneered a bunch of new techniques for effects, and pushed boundaries of what was possible. The original Star Wars has one, repeated, computer-generated sequence in the whole film (the Death Star plans). Everything else was done with practical effects, models, and the techniques listed above. For example [here](https://lumiere-a.akamaihd.net/v1/images/image_e74da0c7.jpeg) is a picture of legendary artist Ralph McQuarrie painting a matte painting for use in ESB (from [here](https://www.starwars.com/news/empire-at-40-5-amazing-matte-paintings-from-star-wars-the-empire-strikes-back)). The black parts are where the live action footage will go [for the final image](https://lumiere-a.akamaihd.net/v1/images/image_4ccf1d80.jpeg). Many of the [epic shots](https://www.reddit.com/r/StarWars/comments/8zol2r/before_the_invention_of_cgi_star_wars_used_matte/) in Star Wars were [made up mostly of paintings](https://www.artofvfx.com/discoveries-from-inside-matte-paintings-unveiled/), [with a bit of actual footage](https://www.starwarsnewsnet.com/2016/04/the-magic-of-the-original-starwars-trilogy-matte-painting-artists.html). Not all of them hold up, but they worked at the time.
Citizen Kane made heavy use of different types of special effects, one of which is an optical printer, where multiple images can be combined/exposed on the same frame, for the purposes of titles, fades, compositing different images together, etc. You can even spot a pteradactyl in one scene being reused from another movie in a Xanadu scene using this technique. Roger Ebert’s commentary breaks down a ton of the special effects.
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