Puer tecum in horto ludere vult.

Because puer is the subject of the sentence: it is the one doing the wanting.

• puer = the boy
• nominative singular of puer, pueri

In Latin, the subject is usually put in the nominative case.

With the pronouns me, te, se, nobis, vobis, the preposition cum is usually attached to the end:

• mecum = with me
• tecum = with you
• secum = with himself / herself / themselves
• nobiscum = with us
• vobiscum = with you all

So tecum is the normal Latin word order here, even though in English we translate it as with you.

Because it follows the preposition in in the sense of in or inside a place.

• in + ablative = in / on a place
• in + accusative = into / onto a place

So:

• in horto = in the garden
• in hortum = into the garden

Here the sentence describes location, not movement, so Latin uses the ablative: horto.

Because it depends on vult.

The verb velle (to want) is commonly followed by an infinitive in Latin, just like English often says wants to play.

So the structure is:

• vult = wants
• ludere = to play

Together: wants to play

Vult is the 3rd person singular present active indicative of velle, which means to want.

Its basic meaning here is:

• vult = he wants or she wants

Because the subject is puer (the boy), we understand it here as the boy wants.

Because Latin usually expresses to + verb with a single infinitive form.

In English:

• to play

In Latin:

• ludere

So the idea of to play is already built into the infinitive ludere. Latin does not need a separate word for to here.

Yes. Latin word order is more flexible than English because the endings show each word’s role.

For example, these would still mean roughly the same thing:

• Puer tecum in horto ludere vult.
• Puer in horto tecum ludere vult.
• Tecum puer in horto ludere vult.
• In horto puer tecum ludere vult.

The original order is perfectly natural, but changing the order can shift emphasis.

Because semantically it makes best sense with play:

• to play with you

Latin often leaves these relationships to meaning and context. Grammatically, tecum could be understood with the whole idea, but in practice the natural sense is:

• The boy wants [to play with you] [in the garden].

So tecum and in horto both describe the infinitive action ludere.

Classical Latin has no definite article like English the, and no indefinite article like a/an either.

So:

• puer can mean boy, a boy, or the boy
• horto can mean garden, a garden, or the garden

The exact sense depends on context. In a normal translation, the boy and the garden are often the most natural choices.

You would usually look them up like this:

• puer → puer, pueri = boy
• tecum → from tu, tui = you
• horto → hortus, horti = garden
• ludere → ludo, ludere, lusi, lusum = play
• vult → from volo, velle, volui = want

This is useful because Latin words often appear in sentences in forms different from the dictionary entry.

Ludere has a fairly broad range of meanings, including:

• to play
• to amuse oneself
• sometimes to play a game
• in some contexts, even to jest or to mock

In this sentence, with puer (boy), the most natural meaning is simply to play.

A simple classroom pronunciation would be:

Poo-er teh-koom in hor-toh loo-deh-reh woolt

More carefully:

• puer = PU-er or PU-wer depending on pronunciation system
• tecum = TE-kum
• in horto = in HOR-to
• ludere = LU-de-re
• vult = wult or vult, depending on whether v is pronounced like English w in your system

In restored classical pronunciation, v is usually like w.

Yes. Volo / velle can sometimes be translated as want, wish, or be willing depending on context.

Here, the most natural translation is:

• wants to play with you in the garden

But wishes to play with you in the garden would also be grammatically possible, just slightly more formal in English.