Why is "Tell the story again" correct? How? Doesn't "tell" often take a person? Shouldn't it be "say" without person?

You can tell someone something. You can tell someone a story. You can tell (someone) a story. You can tell a story. A "story", a "lie", a "tall tale", and others are all types of things that you tell, not people you tell them to, but they can go right after "tell" without a person. In these sentences, the focus is on the information, not on who is learning the information. "I watched her tell a story about..." is basically like saying "i watched her tell whoever was listening to her at that time a story about..."

A book, show, film or person can tell a story. Say means something slightly different. Tell is to convey information to another person. Say means speak but the content could be anything.

I’m have a hard time exactly understanding what your question is, so I’m going to try and answer what I think you’re asking. In English you can have implied subject words. Basically if the speaker thinks it’s obvious what the subject of the sentence is they can just omit it. In the example you gave “tell the story again” it’s assumed that the subject is whoever you are speaking to. It would be just as valid to say “you, tell the story again” or “John, tell the story again”, but it is not needed in this sentence. It can sometimes be hard to determine when you can or can’t omit the subject, so if you’re not sure, it’s best to still say it

In this case “the story” is the direct object. There is usually an implied indirect object (the audience), but not always.

*Tell* can take certain nouns as a direct object. Tell the truth, tell a lie, tell a story, tell a joke.

When stories are performed or presented they are told. You don't say a story really. I think it's from older English because a telling is an archaic noun for a story presentation.

There's no context I can think of in English in which you can "say" a story.

A verb such as "tell" can take two objects. We call them the direct object (DO) and the indirect object (IO). The DO is often a thing that is the result of an action; the IO is a person who is served by the action. If the IO is stated second, it is usually put in a prepositional phrase. "Cameron painted a picture for Stacy." DO is picture, IO is Stacy. When the IO is stated first, it goes without a preposition. "Cameron painted Stacy a picture" means the same thing. "Tell your kids a story" or "Tell a story to your kids" both mean the same thing. The IO is more optional than the DO. I can say "Cameron painted a picture" without saying who was the recipient of the picture, so I can say "Tell the story" without naming the IO, who you're telling. Grammatically, you can't leave off the DO of these transitive verbs. "Cameron painted" is incomplete. However, in speech, sometimes the DO is implied and not spoken. If you say, "I know a joke" I might reply "Tell me," because you understand the complete sentence would be "Tell the joke to me."

“Tell” is a little weird. It allows a double direct object: You can tell someone something. Tell me the truth, tell them a story, tell him a lie, tell her what happened. You can also make the person being told an indirect object: Tell the story to them. *Either* object can be omitted. So “Tell me the truth,” can become either “Tell the truth,” or “Tell me.” Then there are a bunch of weird little exceptions, like how “Tell him what happened,” works but “\*Tell what happened,” doesn’t. You have to “Say what happened.” But you can’t “\*Say the story,” only tell it. I don't know any rule for them. You just have to memorize the special cases. Sorry!

"Tell" can take objects, and it is used over "say" likely because "tell" implies more describing, explaining, intricacy, etc.

Holy crap this direct snd indirect ovject pronoun stuff is so confusing i thought only Spanish had it snd u cant understand it as a native english

I am not sure why, but you can't "say a story." You can only "tell a story." Thinking about the things you say versus the things you tell... I am honestly not sure what puts each in each category. You recite a poem, tell a story, say a prayer, give a lecture – and they mostly don't work if you switch the verbs around.

"Tell the story again" has an implied object. "Tell the story (to me/us/them) again".

Tell has different meanings.  Three are: Talk to someone  Utter something (in general) Give away information Tell him that his nose twitching is a tell for when he decides to tell a lie.