Kumusta? --
How are you? This is the usual Filipino greeting. Respond by saying "mabuti."
Magandang umaga/hapon/gabi. -- Good morning/afternoon/evening.
Mabuhay! -- Long live! This is used as a greeting or as a cheer. Probably related to the spanish "viva".
Paalam -- goodbye. Paalam is a bit formal though, sometimes used for dramatic effect. Normally people just say "sige", the meaning of which is closer to "alright then".
Anong pangalan mo? -- What is your name? Some people say "Sino ka?" (who are you) but it is generally considered impolite.
Ang pangalan ko ay X. -- My name is X. You can also say "Ako si X" -- I am X.
Note on
Filipino vowels. There is only one way to pronounce Filipino vowels, and they are "short" ie "a" should be pronounced as in "can" not "cane". U though, is closer to "oo" than the short u.