Below are some informal ways to say hello and goodbye to each other.

Hello.	Merhaba.
Hello.	Selam.
See you.	Görüşürüz.
Goodbye.	Hoşça kal.
Goodbye.	Güle güle.

Güle güle is an abbreviation of Güle güle git, which literally means go laughing. Therefore güle güle is only said to the person(s) leaving. If you are leaving yourself, you shouldn't use güle güle. Hoşça kal literally means stay pleasantly and is therefore more appropriate to say to the person staying.

Below are some more formal ways to say hello and goodbye to each other.

Good morning.	Günaydın.
Good day.	İyi günler.
Good evening.	İyi akşamlar.
Good night.	İyi geceler.

Günaydın is only used for saying Hello and the other three can be used for saying both Hello and Goodbye. For saying Hello the last three alternatives are particularly polite, and most people use Merhaba instead, which is slightly less informal than saying Selam.

Breakdown of Merhaba.