Verujem svom saigraču.

Verujem is the 1st person singular present tense of the verb verovati. It means I trust / I believe depending on context.

Because the verb ending already shows the subject, Serbian can leave out ja.

Serbian often drops subject pronouns when they are already clear from the verb form.

So Verujem svom saigraču is a natural way to say it, while Ja verujem svom saigraču would usually add emphasis or contrast, such as:

• Ja verujem svom saigraču, a ti ne.
• I trust my teammate, but you do not.

It is in the dative singular.

The verb verovati normally takes the dative when you mean trust someone or believe someone. That is why you get:

• verujem prijatelju
• verujem profesoru
• verujem svom saigraču

Because saigraču is the dative singular form of saigrač.

The base form is saigrač. After verovati, Serbian uses the dative, so the noun changes form:

• nominative: saigrač
• dative: saigraču

If you used saigrača, that would be a different case, not the one this verb requires here.

Because Serbian normally uses the reflexive possessive svoj when the possessor is the same as the subject.

Here, the subject is I, and the teammate belongs to that same person, so svom is the usual choice:

• Verujem svom saigraču = I trust my own teammate

Using mom is generally less natural in standard neutral usage when the possessor is the subject.

Svom is a form of svoj, the reflexive possessive pronoun.

In this sentence, it is:

• dative
• singular
• masculine (agreeing with saigraču)

So svom matches saigraču grammatically.

They agree in the same grammatical features required here:

• dative
• singular
• masculine

That is why you have:

• svom saigraču

If the noun changed, the possessive would change too. For example, with a feminine noun:

• Verujem svojoj saigračici

Because verovati can take the dative directly, without a preposition, when you mean trust someone or believe someone.

So Serbian says:

• Verujem svom saigraču

not something like Verujem ka... or Verujem za...

A useful contrast is:

• verovati nekome = trust / believe someone
• verovati u nešto/nekoga = believe in something/someone

Yes. Serbian word order is fairly flexible.

The neutral order here is:

• Verujem svom saigraču.

But you can move things for emphasis:

• Svom saigraču verujem. = emphasizes my teammate
• Ja verujem svom saigraču. = emphasizes I

The basic meaning stays the same, but the focus changes.

The dictionary form is saigrač.

It means teammate and is built from:

• sa- = with, co-
• igrač = player

So the literal idea is something like co-player, which becomes teammate in natural English.

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

Whether the meaning is a teammate, the teammate, or my teammate is understood from context and from words like svom.

So svom saigraču already tells you enough without an article.