Learn Italian: Vogliamo usare il tuo trapano e il tuo martello, ma non ce li presti. - We want to use your drill and your hammer, but you are not lending them to us.

You are right that "to us" is usually ci. However, when an indirect object pronoun (like ci) combines with a direct object pronoun that starts with 'l' (lo, la, li, or le), the i changes to an e. Therefore, ci + li becomes ce li (to us + them).

What exactly does li replace in this sentence?

li is the direct object pronoun for "them" (masculine plural). Here, it replaces the things you want to borrow: il trapano (the drill) and il martello (the hammer). Because you are talking about two masculine items together, they form a masculine plural group, so we must use li.

Why do the combined pronouns go before the verb presti?

Just like single pronouns, combined pronouns are placed immediately before the conjugated verb they belong to. They act as a single block. Notice that in a negative sentence, the non is placed right before this pronoun block: non ce li presti.

Do I really need to repeat il tuo for both the drill and the hammer?