What you really need to do is listen to as much as you possibly can; immerse yourself in the music, and try gradually to develop an understanding of it that way.  "Celtic" is a rather misleading term as applied to musical styles; the more you hear, the more you will realise that!  Irish music is of course only a part of it.  So far as the singing tradition is concerned, most of it was, traditionally, unaccompanied, so you probably will have trouble finding guitar tab for songs like The Wee Weaver -there are midis of two versions of the tune, by the way, at the Mudcat Midi Site;  click here.  For some very useful information on the use of guitar in Celtic-style music, have a look at  Han's DADGAD Guitar Page.

Good luck,and have fun with the long, but infinitely rewarding, learning process.  Remember; any idiom is best learned through experience rather than by precept.

Malcolm