I say 'Jal ja = Good night' and 'P(*aspiration)uk ja = sleep tight' to close friends.
You can add 'yo' at the end of those stuff to make it formal(still informal as compared with 'Annyeonghi jumuseyo')
If you haven't picked up the Korean alphabet, check out this website.
http://www.korean.go.kr/hangeul/cpron/main.htm
This one is for improving Korean vocabulary.
http://www.wordshowers.com/index.html
And it's good for intermediate or advanced Korean learners, I think.
http://www.teenkorean.net
Note : I notice some Korean learners have got confused with my previous answer about learning the Korean alphabet from the beginning. I'd just like to draw some lines here. Learning the Korean alphabet from the beginning, I find it to get obsessed with the Korean alphabet easily. For example, if you learn the Korean alphabet without listening to the pronunciation, you could soon get confused why 바보 sounds like 'pabo' even though the first ㅂ and the last ㅂ are the same consonant. Also we speak our native languages with our own accents. If a Spanish person learns the alphabet of the second language first, the one could speak the second language with Spanish accent. It's why I think that way. It's just my personal opinion. Don't take it too seriously, there's personal difference in the ability to learn foreign languages.