How to greet:
Günaydın. = Good morning.
İyi günler. = Good day.
İyi akşamlar. = Good evening. (also when you leave)
İyi geceler. = Good night.
Hoş geldiniz. = Welcome. (literally: "you come with pleasure")
Hoş bulduk. = literally: "it's pleasure we found", which is the answer to "hoş geldiniz"
Selamun aleyküm. = from Arabic: May peace with you! (Ve) Aleyküm selam. = Reply: (And) May peace with you!
This kind of greeting often is used when for instance greeting a group of men. It's not usual to greet women this way.
More colloquial ways of greeting are for example:
Selam. = Hello.
Merhaba çocuklar. = Hey guys.
TO SAY GOOD BYE:
Allaha ısmarladık. = Goodbye. (says the one who leaves, literally: "to God we have been ordered")
Güle güle. = Goodbye. (replies the one who remains, literally: "with a smile")
Görüşmek üzere. = Goodbye. (litarally: To see you again)
Hadi, bana eyvallah. = Well, bye from my part.
Hadi, ben kaçıyorum. = Okay, I'm out of here.
hadi is a short form of haydi which means actually something like "come on", "let's go"...
HOW ARE YOU'S:
Nasılsın(ız). = How are you (plural/polite form)?
İyi, teşekkür ederim. Ya sen (siz)? = Thank you, I'm fine. And you (plural/polite form)?
Instead of teşekkür ederim you can also say sağ ol(un).
Other expressions of "how are you":
Ne var ne yok? = What' up?
Ne haber? = What's new?
İyilik. = literally: The goodness. (this are for example the news)
Şöyle böyle. = Regular.
Görüşürüz. = See you. (when saying goodbye)
Bol şanslar. = Good luck.
İyi yolculuklar. = Have a nice trip.