How did you first learn your mother tongue? Did you sing songs or did you play games?
It's similar in Japan. Here is a video clip of a Japanese song for kids to remember everyday greetings. (It can be fun for adults too!) When I was a child there was a very popular kids TV show in Japan called "Hirake Ponkikki" and this song was from that show. I remember as a kid I listened to the song as well as many others from the show as my parents bought me a cassette tape set (Geez, CASSETTE TAPE!).
Surprisingly I still can sing this song off by heart, so I hope this song makes Japanese greetings stuck in your head!
List of greetings appear in the song
Ohayoo - Good morning (casual)
Oyasumi - Good night (casual)
Konnichiwa - Hello
Konbanwa -Good Evening
Itte kimasu -I'm off
Itte rasshai -See you later (when you see someone off)
Tadaima - I'm back
Okaeri nasai -Welcome back
Itadaki masu -I humbly receive (bon appetit)
Gochisoo sama - I appreciate the meal I just had (literally: It was a feast)
Arigatoo - Thank you
Sayoonara - Good bye
Mata ashita - See you tomorrow
(Although it's not a greeting....)
Kinoo no yumeno tsuzuki wo mini ikoo
-Let's go to sleep to continue the dream from yesterday (last night)