In general 'narzędnik' answers the question with whom / with what?
For example: 1. Z kim idziesz do kina? Who are you going to the cinema with? Idę z Anią. I am going (there) with Ania. Z kim? Z Anią.
2. Z czym pijesz kawę? How do you like your coffee? Literally: What do you drink coffee with? (Piję kawę) z mlekiem / z cukrem. (I drink coffee) with milk / with sugar. Z czym? Z mlekiem / z cukrem.