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As several other questions already mentioned, graded readers are a good resources for extensive reading, at least for people who are not yet sufficiently proficient to read texts written for native speakers of the target language.
For smaller languages such as Hungarian, learning resources, including graded readers, are harder to find than for big languages such as English, Chinese and Spanish. Hence this question: are there any graded readers for Hungarian?
600 pages of graded texts, related questions and exercises for each text, 56 of them. Steep learning curve and not for absolute beginners
https://fsi-languages.yojik.eu/languages/FSI/Hungarian/Graded%20Reader/
If that is too much for you, start by reading narratives at the end of the lessons from these textbooks. At the beginning of the each lesson there's also a dialog that helps you put the new words in context. There are two books with 12 lessons each. You start at "good morning" and you finish with B1-B2 level of knowledge. Books are little boring, repetitive and outdated, but the curriculum is excellent.
https://fsi-languages.yojik.eu/languages/FSI/Hungarian/Basic/
I found an online bookshop that claims that the following two books are graded readers:
However, the second book is a novel from 1901 that has been translated into English as Slave of the Huns. Unless it has been simplified for learners of Hungarian, this is not a graded reader. (The bilingual edition published by Bobbs-Merrill in 1969 would not qualify as a graded reader, either.)
I'm Hungarian but I don't really think that there are too many graded readers, but I can suggest you the Magyar Elektronikus Könyvtár (MEK, Hungarian Electronic Library), where you can find many books for free and other texts. MEK has a section for youngers and kids. Maybe these books use simpler language than a typical Hungarian text.
