Learn Russian: Мы часто слушаем музыку.

Слушаем comes from the verb слушать (to listen). For regular first conjugation verbs (verbs ending in -ать), you drop the -ть and add -ем to match the pronoun мы (we). So, мы + слуша- + -ем becomes мы слушаем (we listen).

Why is there no word for "to" in this sentence?

In English, we say "listen to music." But in Russian, the verb слушать doesn't need a connecting word (preposition). It acts right on the object, so you literally just say "we listen music."

Why is it музыку instead of the dictionary form музыка?

Because the music is the direct object—the thing you are listening to. In Russian, this means it needs to be in the accusative case. For feminine nouns ending in -а like музыка, the -а changes to -у when it is the direct object.

Do adverbs like часто always have to go before the verb?

Russian word order is quite flexible, so you could put часто (often) at the end of the sentence and say Мы слушаем музыку часто. However, putting frequency words right before the verb is the most standard and natural-sounding way to say it.