I have always wondered, how do actors memorize very long scripts? Do they somehow read them or is it an absolute must to have an incredible memory to become an actor?
Unless they're performing in a play, actors don't generally memorize the entire script before the film starts shooting.
The reality is, the film will take (on average) 6-12 weeks (or more) to film and the script will likely change constantly. While it's certainly good for an actor to be very familiar with the script so they know what's going to happen, the reality is, many actors memorize a few days' worth of script and work on it in rehearsals or in their private time... and some show up to set without it memorized at all... or reviewed... don't ask me how they survive. I think it's magic or something.
When you only need to do 1-3 pages worth of script in a day, you have plenty of time to memorize.
In general, actors do have good memories... and part of their training is honing this ability... but good actors know the gist of what they're saying and the words should be natural to them, not "learned by rote". Many directors want natural performances and give actors some leeway to work inside the script a bit so that it feels natural to their character.
Memory is one of those things that gets better as you use it... if you practice memorizing things, you will get better at it. It's how servers at restaurants can memorize convoluted orders and still get everything right... they have practice memorizing stuff.
In a movie, you typically don't need to learn the whole script. You just need the current scene, and that's usually just a few lines - easy to learn on the spot. Most of the practice is spent finding good ways to express yourself, I'd guess. And worst-case scenario, you just wasted a take - you can (almost) always just try again, and leave picking the best movie to the director and the cutting room :)
Plays are different, because there's no takes to save you when you make a mistake. I've played in a few 2 hour long plays, so I can tell you... it's easier than it sounds. You just practice a bit and get the whole thing. As UncleZeiv noted, dialogues are much easier to remember - there's a certain pattern to follow. In older dramas, heavier on monologues, you'll often see the same thing - outright rhymes, or other patterns to follow (it basically serves as error correction). It's similar to how it's easier to remember every other line of a song - more connections for the brain to pick up, and more patterns to fill. Human brains are really good at finding and repeating patterns. Remember how much easier it was to learn something you understand, as opposed to just memorizing data that seems random to you?
Even when the data is outright random, this still applies. For example, remembering a phone number, you might give yourself hints like "three sixes and a one..." - our brains love patterns, even when there aren't any in the data. The same way, with a long monologue with nothing to help you (which is often a result of an amateur screenwriter, frankly :P), you'll try to find something to help you keep and link those memories. There's many approaches to memorizing stuff that doesn't make any sense - it's just a google search away. But basically, you want to split the text into logical pieces (partitioning - one of the reasons we use paragraphs), practice each part, and practice the whole thing. Adding emotions and images helps immensely - memories work best when you have multiple different "paths" to get to the piece of data you're trying to retrieve. So by playing around with the monologue, you'll have the part where you're agitated, and the part where you're angry, and the part where you're affraid (Harpagon is one good example of a rather long monologue where this technique helps immensely).
And when something goes wrong and you forget a bit, it's not the end of the world. Most of the time, you'll just ad-lib something to keep the flow, and work your way around it (again, works great for dialogues, where your partner can support you, or even outright point out what you were supposed to say - in a smart way, hopefully). This is especially true when you're not doing classical plays - in fact, when you're playing your own plays, a lot of the material can come from errors, or spur-of-the-moment ideas that just fit the moment. It's the same in (amateur-level :P) music production - pressing the wrong key isn't necessarily something anyone will notice, just keep playing and don't show your fear :D
Don't forget that for most of human history, the default way of transmitting stories was play (sure, you recited poetry - but adding and expressing emotions is still a huge part of recitation). We've been doing this for thousands of years, maybe tens of thousands. Even "books" like the Bible were originally mostly spread by spoken word, and the same goes for ancient epics like the Illiad. Written word was rare and expensive before mass printing.
In short, there's three main points: practice, patterns and links (emotions, gestures, images...). Relevant comic link: https://xkcd.com/936/ :)
There is at least one example of a prominent, A-list actor, Marlon Brando, who did not memorize his lines. Cue cards were printed with his lines and he would read from them.
This article discusses some of the tricks used in The Godfather:
There is even a picture of Robert Duvall holding cue cards on his torso so that Brando could read them.
Bob Hope was also one who used cue cards, as he had grown used to holding a script when he started out in radio. When he transitioned to television, he used cue cards.
Though you may not believe it, top actors are very intelligent and usually have excellent memories. Just as one example, when Alec Baldwin played Jack Ryan in 1990's "Hunt for Red October" he had to give a long speech in Russian. In an interview 10 years later, Baldwin was asked about remembering lines and he explains he always had an excellent memory and to prove it he recited the sentences in the Russian language from The Hunt for Red October flawlessly.
Many actors and actresses are known for their extensive practice and memorization of lines. For example, Meryl Streep was known for working non-stop 16-hour days whenever she worked on movies, and much of that time was spent practicing and memorizing lines. Jody Foster is known for having similar dedication.
I believe that ancient Romans gave long structured speeches by imagining that they are walking through rooms in a familiar building, in a particular order, and recalling what they see in each part of each room.
Although I am not proficient in this technique, perhaps a person today could imagining walking into one room and seeing on the first computer monitor in one room: Friends, Romans, Countrymen each holding bags of ears. A shovel and a grave with Cesar lying in it; a red x painted on a heroic bust of him. A symbol of evil (I would use a black cloud with cartoon lighting coming out) floating over a closed grave, the word good mixed with bones in a half filled grave.
Simply constructing the story with vivid images might go a long way to memorizing it.
I no longer have it word for word -- need to refresh my memory -- but I memorized a short story that runs about an hour in performance. (Brightly Burning Tiger by Tanith Lee), just because I liked the tale and wanted to be able to tell it.
First step is to put it in perspective. A typical non-pop song is three to five minutes. So just in terms of time, this is like learning 12-20 songs. Admittedly, most songs are less dense, so perhaps double that.
True, songs have rhythm and rhyme and repeated phrases and other formalisms which aid in structuring memory... But a good script or story often has strong characters who each have their own "voice", and the author has a particular writing style; combining those with the plot and situation, and there are patterns that affect which words sound "right" at any time, which helps to support the learning process. And I selected this story and it's set of roles because these aspects were clear enough that the tale had stayed with me.
(In fact, actors are taught to "leave the words on the page", and recreate them based on what they think the character would say in that situation... and the effects I've just mentioned help to keep them "on script" without having to remember every word separately. Which is a good thing since it leaves most of heir attention free to play the role.)
Looking at it from another perspective, when I retyped the story for study, it came to 12 single-spaced pages. That also sounds much less overwhelming than an hour of speech. Remember, there's usually plenty of rehearsal time and you don't have to memorize the whole thing at once or immediately.
Rehearse, rehearse, rehearse. As with music, "play through" any mistakes,since you are still building the memories for the rest. Practice makes better. Simply making the time to rehearse is a huge part of the process. My cat at the time way very happy that I was spending an hour most nights sitting with her in my lap, making (mostly) friendly-human noises.
It didn't take very long to get to the point where I could tell the tale in general outline, forgetting details and having to search for my own words in places. The next step was more directed rehearsal, marking up the script to indicate where I was leaving things out or saying them differently than Ms. Lee had.. Practicing those phrases in isolation, like learning a riff on an instrument, helped knock out those errors.
Once I had it, all I had to do was refresh it every so often by telling the story, and I could start fine-tuning voices and timing, and getting my voice keyed up to the proper level of tension at the pivotal points in the story. For quite some time I was practicing this on every long drive, in the shower, and using it as a "bedtime story" for myself. It's quite satisfying, and does feel more like reading it or listening to someone else perform it... Again, that's the "leave the words on the page" effect; the story largely tells itself once started. There is mention in another answer of the "memory palace" technique, and this is much the same; each scene reminds me of the next.
As I say, it's been a while and there are once again places where I know I no longer have the exact words... But I could get back that level of precision relatively quickly if I wanted it; most of it is still there. And that, ultimately was the goal; I wanted to be able to drop into character and tell the story, as faithfully as possible, but while making it my own (as much as the character's differences from me permit).
Humans are much more talented than we usually give ourselves credit for. Skill/talent is half of it, but believing you can do it is the other half. And practice time is the third half :-D
It's their job. On film sets, you usually only need to remember those parts of the script that are taken.
To put it into perspective, there are several theatre pieces (like Süskind's "Double Bass") where a single actor delivers a soliloquy of more than hour-long duration. Obviously, you have to learn this in context, following a sequence of themes rather than just streaming words together.
Stuff like the Iliad and Odyssey survived for centuries through only oral tradition: the performers learnt the epics over the course of years and then made their living, partly travelling, as live recordings.
For theatre, being able to learn your part is an acquired and practiced and indispensible skill. For film, it's still important but in a different balance with the ability to invest full concentration into single takes.