This post will go over one of the common ways to describe things or people in Hungarian.

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milyen = how, what kind of, like what?

For people, milyen is used to ask what someone is like, what kind of person they are – i.e. their personality, how they behave, or comparing them to something else.

For things, milyen is used to ask what the thing is like, or what kind of thing it is – i.e. is it interesting, how did you like it, was it good/bad, or comparing it to something else.

Examples

Milyen az új tanár az iskolában? (What is the new teacher at the school like?)
literally: how is/what kind of (person) is the new teacher at the school

Milyen volt a film? (How was the film/What was the film like?)

Szerinted milyen az új Stephen King-könyv? (In your opinion, how is the new Stephen King book?)

Mexicó mentél?! Milyen volt? (You went to Mexico?! How was it?/What was it like?)

You can combine milyen with descriptive terms in order to describe color or other specific qualities.

Milyen színű a szemed? (What color are your eyes?)
literally: how are your eyes colored

Milyen haja van a férjednek? (What kind of hair does your husband have?) – this can refer to the style (curly, straight, etc), or to the color.

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olyan = like that, that kind of, such as that

olyan is used for things that aren’t necessarily close in proximity to you. It can be the idea of something, a past or former thing, or something at a different location.

Examples

Olyan macskát szeretnék, ami az ölembe ülne (I would like a cat that will sit in my lap)
literally: I would like the kind of cat, that would sit in my lap

Az anyám olyan, hogy nem bírja a sírást (My mother is the kind of person who can’t stand crying)
literally: my mother is such that, that she can’t stand crying

A nagyim olyan országban lakott, ahol este a nők nem tudtak szabadon járni (My grandmother lived in the kind of country where women couldn’t walk about freely at night)

Az anyám olyannak¹ nevelt, hogy mindig próbálok kedves lenni (My mother raised me to always try to be kind)
literally: my mother raised me such that, that I always try to be kind

¹-nak is added here, because you are saying your mother raised you (in)TO that kind of person

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Olyan with mint and hogy

You can also use olyan to compare things or describe to what extent something is. You will often see “olyan….mint” (as…as…) as a construction used to compare things.

A barátnőm olyan gyönyörű, mint egy angyal (My girlfriend is as beautiful as an angel)
literally: my girlfriend is (that kind of) beautiful, like an angel

Olyan unalmas volt a film, hogy majdnem elaludtam (The film was so boring that I almost fell asleep)

Olyan cuki vagy, mint egy kiscica (You’re as cute as a kitten)

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ilyen = like this, this kind of, such as this

While olyan can refer to things not immediately present, ilyen is more appropriate for something closer in proximity – i.e. something you’re currently talking about or seeing

Person A: Az én munkahelyemen, két hónap szabadságot kaphatsz (At my job, you can get two months of vacation)
Person B: Na, nekem is kell ilyen munka (Wow, I also need a job like this)

Person A: Szeretnék olyan országban lakni, ahol a kormány hallgat a polgáraira (I would like to live in (such) a country, where the government listens to its citizens)
Person B: Szerintem nincs is ilyen ország (I don’t think that such a country exists)
literally: In my opinion, there is no country like this

Ilyen cuki vagy, mint ez a kiscica (You’re as cute as this kitten) – referring to a kitten that is currently present/in view, rather than a theoretical one

Most miért vagy ilyen bunkó? Általában olyan¹ kedves vagy. (Why are you being such a jerk right now? You’re usually so kind)

¹olyan is used in the second part here, because you’re referring to previous/other behavior that you’re not currently seeing, whereas ilyen is referring to the behavior currently on display.

Ilyen ruhában akarsz elindulni? Legalább egy dzseki kell. (Are you leaving/heading out in clothes like these? You at least need a jacket)

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In Summary

milyen = WHAT kind of, WHAT is it like
-can be used with any noun to ask about appearance, traits, behavior, personality, etc.

olyan = THAT kind of, like THAT, such as THAT
-can be used with any noun to describe or emphasize appearance traits, behavior, personality, etc.
-used for things that aren’t immediately present or visible

ilyen = THIS kind of, like THIS, such as THIS
-can be used with any noun to describe or emphasize appearance, traits, behavior, personality, etc.
-used for things that are currently present/visible, or were recently mentioned