Magic The Gathering Question?

Hi, I'm pretty new to MTG and I have a question regarding the -1/-1 counters. Say my opponent has a 2/2 creature out on the battlefield, and I have an instant spell that puts -2/-2 counter on that creature until the end of the turn. Does it mean then that the creature is 0/0 for 1 turn but it comes back to normal the next turn, or it dies since it's toughness reaches 0? If it remains on the battlefield, then what in case of instant with -3/-3, that creature would drop to -1/-1 would it die then? Thanks!