Learn Italian: Nella bottega, si è lavorato il cuoio con le mani. - In the workshop, people worked the leather with their hands.

You are right that lavorare normally uses avere (for example, lui ha lavorato). However, when you add the impersonal si to mean "people in general" or "one", the helping verb always shifts to essere in compound tenses like the passato prossimo.

Why does lavorato end in -o here? Is it agreeing with something?

Yes, it is agreeing with il cuoio, which is masculine singular. When an impersonal si sentence has a direct object, it acts like a passive construction and the past participle must agree with that object. If the object were feminine, like la pelle (the leather/skin), the verb would change to match it: si è lavorata la pelle.

The English translation says "with their hands", but the Italian uses con le mani ("with the hands"). Why is there no possessive word?

In Italian, you typically use definite articles (like le) instead of possessives (like le loro) for body parts when it is obvious who they belong to. Even with the impersonal si, le mani naturally translates to "their hands" or "one's hands".

Why does the sentence start with nella instead of just in?