Learn Hardcore Hungarian: Ez nem probléma.

Stress is always on the first syllable of each word: EZ nem PRO-blé-ma.
e (in ez, nem) is like the e in bet.
é (in probléma) is a long closed e, like the vowel in café, but not a diphthong.
Final a (in probléma) is a short back vowel, similar to the o in British hot.
r (in probléma) is a quick tap.

Why is there no form of the verb to be (van)?

In present tense, third person, when the predicate is a noun or adjective, Hungarian normally drops van. So:

Ez probléma. = This is a problem.
Ez nem probléma. = This is not a problem. You do use van for existence or location:
Van probléma. = There is a problem.
A könyv az asztalon van. = The book is on the table.

Can I say Ez nem van probléma?

No. That is ungrammatical. Say:

Ez nem probléma. = This is not a problem. (classification) Or, for existence:
Nincs probléma. = There is no problem.

What is the difference between Ez nem probléma and Nincs probléma?

Ez nem probléma. denies that this particular thing counts as a problem. It’s about classification of this.
Nincs probléma. states that there is no problem at all (existential). Use it to answer Is there a problem? type questions.

Do I need an article like egy here? What about a/az?

Predicative nouns after an implied copula usually have no article: Ez probléma. / Ez nem probléma.
egy can appear for emphasis or contrast: Ez nem egy probléma, hanem egy feladat. (not a problem but a task)
With a definite meaning use a/az: Ez nem a probléma. (This is not the problem we mean.)

How do I say This is the problem?

Use the demonstrative plus the definite article:

Ez a probléma. = This is the problem. Note Hungarian uses the definite article with demonstratives before a noun: ez a könyv (this book), az az ember (that person).

Where does nem go, and how does word order change the meaning?

Neutral negation: Ez nem probléma. (This isn’t a problem.)
To contrast the subject (it’s not this that’s the problem): Nem ez a probléma.
To contrast the predicate (it’s not the problem, but something else): Ez nem a probléma, hanem a tünet. The negation nem comes right before the focused element.

When should I use ez versus az?

ez = this (near the speaker): Ez nem probléma.
az = that (farther away or previously mentioned): Az nem probléma. Plurals: ezek (these), azok (those).

How do I say it in the plural?

How do I say It’s not a problem for me?

Use the dative for the person affected:

Nekem nem probléma. More formal: Számomra nem probléma. For other persons: Neked/Önnek/nekünk etc. + nem probléma.

Is it natural to drop Ez and just say No problem?

Yes, in replies you can simply say:

Nem probléma. Even more idiomatic:
Semmi gond.
Semmi baj. As a response to thanks, Hungarians also commonly use Szívesen. (you’re welcome) or Nincs mit. (don’t mention it).

Are there synonyms for probléma with different tones?

How can I intensify or soften the sentence?

Why is it probléma with é, and what’s the difference between a and á?

é marks a long closed e sound; it’s distinct from short e.
a is a short back vowel (like British hot), while á is a long fronted a (like the a in father but longer). Here we have probléma with é and a short a at the end.

Should it be Ez or Ezt here?

Use Ez because it’s the subject. Ezt is the object form: