Moj unuk danas prvi put ide u školu.

Because unuk is a masculine singular noun in the nominative case, and the possessive adjective moj has to match it.

• moj = my for masculine singular nominative
• unuk = grandson

So:

• moj unuk = my grandson

If the noun changed case, moj would usually change too:

• Moj unuk = my grandson
• Vidim mog unuka = I see my grandson

In your sentence, unuk is the subject, so nominative is used.

Croatian normally does not use articles like English a/an/the.

So:

• unuk can mean a grandson, the grandson, or just grandson
• the exact meaning comes from context

In Moj unuk danas prvi put ide u školu, moj already makes the noun definite enough, so English naturally translates it as my grandson.

Danas means today.

It is an adverb, so it works on its own, just like English today:

• Danas radim. = I’m working today.
• Danas je hladno. = It’s cold today.

You do not need a preposition before it.

Prvi put means for the first time.

Literally:

• prvi = first
• put = time / occasion

This is a very common expression in Croatian.

Examples:

• Prvi put sam u Zagrebu. = I’m in Zagreb for the first time.
• Ona prvi put vozi sama. = She is driving alone for the first time.

So in your sentence:

• danas prvi put = today for the first time

Both may be heard, but prvi put is the most common and neutral modern form.

You may also come across:

• prvi puta
• po prvi put

These are understandable, but prvi put is usually the safest and most natural choice for everyday Croatian.

Ide is the 3rd person singular present tense of ići (to go).

Because the subject is moj unuk = my grandson, Croatian uses the he/she/it form:

• ja idem = I go / am going
• ti ideš = you go / are going
• on/ona ide = he/she goes / is going

So:

• Moj unuk ide... = My grandson goes / is going...

Croatian often uses the present tense for something that is happening now, today, or as part of an event that is already scheduled or understood in context.

So ide can mean:

• goes
• is going
• sometimes even is going to go, depending on context

In this sentence, English often translates it naturally as:

• My grandson is going to school for the first time today.

So even though Croatian uses the present tense, the meaning can sound future-like in English.

This is a very important Croatian pattern:

• u + accusative = movement into/to
• u + locative = location in

So:

• ide u školu = he goes to school
• je u školi = he is in school / at school

In your sentence, there is movement, so u školu is correct.

Because after u expressing movement, the noun goes into the accusative case.

The dictionary form is:

• škola = school

But the accusative singular of this feminine noun is:

• školu

So:

• u školu = to school

Compare:

• škola = school
• u školi = in school
• u školu = to school

It can suggest both, depending on context.

In this sentence, prvi put strongly suggests that the grandson is going to school for the first time, which in natural English often implies:

• it is his first day of school
• he is starting school

So the phrase can refer not only to the physical act of going there today, but also to the milestone of beginning school.

Yes, Croatian word order is more flexible than English word order.

This version is natural because it presents the information smoothly:

• Moj unuk = topic
• danas = time
• prvi put = important circumstance
• ide u školu = main action

Other orders are possible, for example:

• Danas moj unuk prvi put ide u školu.
• Moj unuk prvi put danas ide u školu.
  This one can sound slightly different in emphasis.

Croatian often changes word order for focus, emphasis, or style, not because the basic meaning changes much.

Yes, Croatian often leaves out possessive words when the meaning is clear from context.

So you could say:

• Unuk danas prvi put ide u školu.

But that would usually sound more like:

• The grandson / grandson is going to school for the first time today

Using moj makes it specifically my grandson and gives the sentence a more personal, explicit feel.

A simple pronunciation guide for an English speaker:

• Moj ≈ moy
• unuk ≈ OO-nook
• danas ≈ DAH-nahs
• prvi ≈ PUR-vee or PR-vee
  (the r can act almost like a vowel)
• put ≈ poot
• ide ≈ EE-deh
• u ≈ oo
• školu ≈ SHKO-loo

A rough full version:

• Moy OO-nook DAH-nahs PUR-vee poot EE-deh oo SHKO-loo

A few useful sound notes:

• š sounds like sh in ship
• u is like oo in food
• Croatian words are usually pronounced clearly and consistently, much more phonetically than English

Yes. Unuk specifically means grandson.

Related words:

• unuk = grandson
• unuka = granddaughter

So the sentence is specifically about a boy.

Here are the basic forms:

• moj = my
• unuk = grandson
• danas = today
• prvi = first
• put = time / occasion
• ići = to go
• u = in / into / to
• škola = school

In the sentence, ide is the conjugated form of ići, and školu is the accusative form of škola.