Proces začne zítra.

Because začít is a perfective verb. In Czech, perfective verbs normally use present-tense forms to talk about the future.

So:

• začne = will start
• literally it looks like a present form, but its meaning is future here

By contrast, an imperfective future would use bude + infinitive or another future construction, but that would express a different nuance. With začít, Czech usually uses the perfective verb for a single completed starting event.

Začne is the 3rd person singular form of začít.

It agrees with proces, which is singular:

• já začnu = I will start
• ty začneš = you will start
• on/ona/ono začne = he/she/it will start

Since proces is a singular noun, the verb must also be singular: proces začne.

Czech often does not need a separate equivalent of English will.

With perfective verbs, the present form usually has future meaning:

• napíšu = I will write
• přijde = he/she/it will come
• začne = he/she/it will start

So English uses will, but Czech often expresses the future through the verb form itself.

Proces is a masculine inanimate noun.

That matters because Czech nouns belong to grammatical genders, and gender affects agreement and declension.

Here, in the nominative singular, it appears as:

• proces = subject of the sentence

Because it is the subject, the verb agrees with it in number, giving začne.

Because zítra is an adverb, not a noun phrase.

It simply means tomorrow and functions like an adverb of time, so no preposition is needed:

• dnes = today
• zítra = tomorrow
• včera = yesterday

So Czech says:

• Proces začne zítra.

not something like v zítra.

Yes. That is completely natural.

Czech word order is more flexible than English because grammatical roles are shown more by endings and verb forms than by position.

Both are correct:

• Proces začne zítra.
• Zítra začne proces.

The difference is mostly one of focus or emphasis:

• Proces začne zítra. → neutral; starts with the subject
• Zítra začne proces. → puts more emphasis on tomorrow

Proces is a normal Czech word, but it often sounds a bit more formal, technical, or abstract, much like English process.

Depending on context, Czech might also use words like:

• řízení = proceeding / management / process, depending on context
• postup = procedure / process
• výroba začne zítra = production starts tomorrow

So proces začne zítra is grammatically fine, but whether it sounds natural depends on what kind of process you mean.

A rough pronunciation guide:

• Proces ≈ PRO-tses
• začne ≈ ZACH-neh (with č like ch in church)
• zítra ≈ ZEE-tra

A few useful details:

• c in Czech is pronounced ts
• č is like ch in church
• í is a long ee sound

So the sentence is roughly:

PRO-tses ZACH-neh ZEE-tra

The infinitive is začít = to start / to begin.

Useful related forms:

• začít = infinitive
• začne = will start
• začal = started (masculine past)
• začala = started (feminine past)
• začalo = started (neuter past)
• začínat = to be starting / to start habitually or repeatedly (imperfective partner)

This pair is important:

• začít = perfective
• začínat = imperfective

In practice, Proces začne zítra refers to the future. In English, starts tomorrow looks like a present form but has future meaning; in Czech, the future meaning comes from the perfective verb form.

So even though začne looks like a present-tense form morphologically, it is understood as future here.

Not much in this particular sentence.

• proces is in the nominative because it is the subject
• zítra is an adverb, so it does not change for case
• začne is the finite verb

So this is a relatively simple sentence structurally:

• subject: proces
• verb: začne
• time adverb: zítra

That makes it a good example of basic Czech sentence structure.