Learn Hardcore Polish: On odkłada słuchawkę, kiedy kończy rozmowę z lekarzem. - He puts down the receiver when he finishes the conversation with the doctor.

Odkłada słuchawkę, kiedy kończy rozmowę… – perfectly correct and very natural
On odkłada słuchawkę, kiedy kończy rozmowę… – also correct, but On adds a bit of emphasis or makes the subject extra clear (e.g. contrasting with someone else: On odkłada, a ona dalej mówi – He hangs up, and she keeps talking).

So the pronoun is optional; it’s used for emphasis, contrast, or clarity, but often dropped in neutral sentences.

What does odkłada literally mean, and is it the normal way to say “hang up (the phone)”?

Literally, odkładać means to put something aside / to put something down.

In the context of phones, odkładać słuchawkę is the standard idiomatic way to say to hang up (the receiver/phone), especially for a traditional phone with a handset.

Some related options you might hear:

odkłada słuchawkę – he puts the receiver down / hangs up
odkłada telefon – he puts the phone down (also used, more modern-sounding)
rozłącza się – he disconnects / hangs up (focus on ending the call, not the physical act)

So yes, odkłada słuchawkę is a normal, natural way to express “he hangs up”.

Why is it słuchawkę and not słuchawka?