Learn Spanish (Latin America): Mi hermano trepaba los árboles en el parque. - My brother would climb the trees in the park.

The imperfect tense is used for past habits or repeated actions. Because this was something your brother used to do regularly (translated here as "would climb"), you use the imperfect ending -aba. If you used trepó, it would mean he climbed the trees exactly one time on a specific day.

The English translation says "would climb". Where is the word for "would" in the Spanish sentence?

In English, we often use "would" to talk about past habits, like "I would visit my grandmother every Sunday." Spanish doesn't use a separate word for this kind of "would." Instead, the imperfect ending -aba in trepaba has this "used to" or "would do" meaning built right into it.

Do I need to use a preposition like a or en between trepaba and los árboles?

No extra preposition is needed here. Just like in English where you "climb the trees," in Spanish you can say trepaba los árboles directly. The verb trepar connects straight to the thing being climbed without needing a connecting word.

The imperfect ending -aba is used for both yo (I) and él/ella (he/she). How do we know who is climbing?