Veterinář přijde zítra.

Because přijít is a perfective verb. In Czech, the present-tense forms of perfective verbs usually refer to the future, not to something happening right now.

So:

• přijde = he/she/it will come
• not usually he/she/it comes right now

If you want a true present meaning such as is coming or comes, Czech normally uses the imperfective verb přicházet:

• Veterinář přichází. = The vet is coming / The vet comes

It comes from the infinitive přijít, meaning to come / to arrive.

přijde is:

• 3rd person
• singular

So it means he/she/it will come.

A useful mini-conjugation is:

• já přijdu = I will come
• ty přijdeš = you will come
• on/ona/ono přijde = he/she/it will come
• my přijdeme = we will come
• vy přijdete = you will come
• oni přijdou = they will come

Because it is the subject of the sentence, so it is in the nominative singular form, which is also the dictionary form.

Here, veterinář means vet / veterinarian and it is a masculine animate noun.

So the structure is basically:

• Veterinář = subject
• přijde = verb
• zítra = time adverb

Czech does not have articles like English the and a/an.

So veterinář can mean:

• the vet
• a vet

Which one is meant depends on the context. In many situations, the listener already knows which vet is being talked about, so English would naturally use the.

Yes. Czech word order is much more flexible than English word order.

Veterinář přijde zítra. is a normal, neutral sentence.

But you can also say:

• Zítra přijde veterinář.
• Veterinář zítra přijde.

These versions are all grammatical, but the focus changes a bit:

• Veterinář přijde zítra. = neutral statement
• Zítra přijde veterinář. = emphasis on tomorrow
• Veterinář zítra přijde. = often contrastive, like the vet will come tomorrow

So Czech word order often shows information structure rather than strict grammatical roles.

Zítra is an adverb of time, meaning tomorrow.

It does not need a preposition here. Czech simply says:

• zítra = tomorrow

That is similar to English, where you also normally say tomorrow, not on tomorrow.

A few key points:

• Czech stress is usually on the first syllable
• á and í are long vowels
• j is pronounced like English y
• ř is a special Czech sound with no exact English equivalent

Approximate pronunciation tips:

• veterinář: stress the first syllable: VE-te-ri-nář
• přijde: stress the first syllable: PŘIJ-de
• zítra: roughly ZEE-tra

About ř:

• It sounds something like an r and the zh sound in measure at the same time.
• If you cannot say it yet, using a normal r at first is completely understandable for learners.

Also, do not confuse stress with vowel length:

• In veterinář, the stress is at the beginning, even though á is long.

Yes, veterinář is grammatically masculine and usually refers to a male vet.

For a female vet, Czech normally uses:

• veterinářka

So:

• Veterinář přijde zítra. = The male vet will come tomorrow.
• Veterinářka přijde zítra. = The female vet will come tomorrow.

In some contexts, masculine job titles can be used more generically, but for a specific woman, veterinářka is the usual form.

Yes, but it is not exactly the same.

• Veterinář přijde zítra. = The vet will come tomorrow

  • a simple future fact
  • one completed arrival

• Veterinář přichází zítra. = something more like The vet is coming tomorrow

  • often sounds more scheduled or arranged
  • uses the imperfective verb přicházet

So přijde is the most straightforward and neutral way to say will come tomorrow.

It can mean either, depending on context.

Přijít often means:

• to come
• to arrive
• to turn up

So Veterinář přijde zítra. could be understood as:

• The vet will come tomorrow
• The vet will arrive tomorrow

English chooses the most natural wording based on the situation.

A simple yes/no question is:

• Přijde veterinář zítra?

Czech usually does not need a helping verb like English does.

So English:

• Will the vet come tomorrow?

Czech:

• Přijde veterinář zítra?

You can also hear other word orders, such as:

• Přijde zítra veterinář?

Intonation helps show that it is a question.