Na stole jsou tři hrnky.

Because stůl is the basic dictionary form, the nominative singular.

After the preposition na when you are talking about a fixed location, Czech uses the locative case, so:

• stůl = table
• na stole = on the table

So stole is the locative singular form of stůl.

Yes. Na can take different cases depending on the meaning:

• location → locative
  Na stole = on the table
• movement onto something → accusative
  Dám hrnek na stůl = I’ll put a mug onto the table

In Na stole jsou tři hrnky, nothing is moving. The sentence only describes where the mugs are, so locative is used.

Jsou is the 3rd person plural present of být, meaning to be.

So literally:

• jsou = are

In this sentence it works like English there are, even though Czech does not need a separate word like there.

So English says:

• There are three mugs on the table

But Czech simply says:

• On the table are three mugs
• Na stole jsou tři hrnky

Because the subject is tři hrnky, which refers to more than one thing.

With dva, tři, and čtyři, Czech normally uses a plural verb:

• Na stole jsou tři hrnky
• Na stole jsou dva talíře

This is useful to compare with larger numbers, because after five and above, Czech often switches:

• Na stole je pět hrnků

So:

• 2–4 → usually plural verb
• 5+ → often singular verb in standard Czech

Because after the numerals dva, tři, čtyři, the noun usually appears in the form that looks like the nominative plural:

• dva hrnky
• tři hrnky
• čtyři hrnky

But after pět and higher, Czech usually uses the genitive plural:

• pět hrnků
• šest hrnků

So:

• tři hrnky = correct
• tři hrnků = not correct

In a normal full sentence, no. A learner should keep it:

• Na stole jsou tři hrnky.

You may sometimes hear or see something like:

• Na stole tři hrnky.

But that is elliptical and sounds like a note, headline, or very casual shortened speech. It is not the safest pattern for learners. In standard everyday sentence building, use jsou.

You can say both, but the emphasis changes.

• Na stole jsou tři hrnky.
  Very natural if you are introducing what is on the table.
• Tři hrnky jsou na stole.
  Also grammatical, but it puts more focus on three mugs or contrasts them with something else.

Czech word order is flexible, and it often reflects information structure:

• known setting first
• new information later

So Na stole jsou tři hrnky is a very natural neutral sentence.

Because Czech has no articles like English a and the.

So hrnky by itself can mean things like:

• mugs
• the mugs
• some mugs

The exact interpretation comes from context, not from an article.

That is completely normal in Czech. You do not need to add anything to mean the here.

Yes, na stole really means on the table, literally on its surface.

If you want at the table, Czech usually says:

• u stolu

So compare:

• Na stole jsou tři hrnky. = There are three mugs on the table.
• Sedím u stolu. = I’m sitting at the table.

This is a very common distinction and worth learning early.

A rough guide is:

• Na = nah
• stole = STO-le
• jsou = roughly ysoh
• tři = tricky; roughly trzhi, but the ř sound has no exact English equivalent
• hrnky = roughly HRN-kee, with the r acting almost like a vowel

A more technical pronunciation is approximately:

• [na ˈstolɛ jsou̯ tr̝̊i ˈɦr̩ŋkɪ]

Two sounds often cause trouble for English speakers:

• ř in tři
• the syllabic r in hrnky

So those are the parts most worth practicing.