Learn French: Le chien a trouvé la balle.

You would say Trouve-la ! Since la balle (the ball) is feminine, we replace it with the pronoun la (it). In an affirmative command, the pronoun attaches to the end of the verb with a hyphen. Also, notice we drop the final -s from the tu form of -er verbs, making it trouve instead of trouves.

Why does the past tense here use a trouvé instead of just a single word for "found"?

This sentence uses the passé composé to talk about a completed action in the past. It requires two parts: a helping verb (here, a, which is the il/elle/on form of avoir) and a past participle (trouvé). While English just says "found," French literally says "has found."

If the dog had found multiple balls, would the word trouvé change?

No, it stays trouvé here. When using the helping verb avoir, the past participle doesn't normally change to match the object coming after it. So, a trouvé la balle and a trouvé les balles both use the exact same spelling for trouvé.