Trovo una cassetta degli attrezzi vecchia in cantina.

Trovo is the first-person singular present indicative of the verb trovare (“to find”). It means “I find.”

• Trova would be third-person singular (“he/she finds”).
• Trovate is second-person plural (“you all find”).
• Trovare is the infinitive (“to find”) and can’t stand alone as the finite verb here.

Una is the indefinite article (“a/an”), indicating you’re finding a toolbox, not a specific one already known to the listener.

• If you said la cassetta, it would be “the toolbox” (a specific one).
• Italian generally requires an article before countable nouns, so you can’t simply say cassetta without one.

Degli is the contraction of di + gli, and you need it because attrezzi (“tools”) is masculine plural starting with a vowel.

• Di
  • i would make dei, but before a vowel (or z/​s+consonant) you use degli.
• This structure shows possession or composition: “a box of tools.”

Adjective placement can slightly change the nuance in Italian:

• Post-nominal adjective (cassetta … vecchia) is purely descriptive: “a toolbox that is old.”
• Pre-nominal adjective (una vecchia cassetta) can feel more subjective or idiomatic, sometimes implying “just an old toolbox” or “that old toolbox.”
  In many contexts the meaning overlaps, but pre-nominal adjectives often carry a more emotional or stylistic tone.

When indicating location with certain place nouns, Italian often omits the article after in (like in chiesa, in piazza, in cantina). It gives a general sense of “in a cellar.”

• If you want to specify a particular cellar, you could say nella cantina (“in the cellar”).
• In una cantina would be “in a cellar,” but using una adds emphasis to it being one among many.