A good way into it, since you are starting as a singer, is to sing a song (which doesn't have a chorus - elsewise the audience will drown you out)and lilt a 'chorus' between each verse. Don't do it with Lord Bateman! Something light and short.

I once heard an Irish builder called Mike Henry do it with this:

She came from the mountains, her stockings were black.
I'd like to be tickling the small of her back.
She came from the mountains her stockings were white.
I'd like to be tightening her garters.

While walking the road to sweet Athy
I saw an old petticoat hanging to dry
So I took off my trousers and left them nearby
To keep the old petticot warm.

Paddy McCarty he had a fine goat
So he tied it up with a rope by the throat.
Along came a fellow and stole off its coat
So now it's another damned bodhran.

I courted a girl and she was quite fair
Her only drawback was her surplus of hair.
She came from Athy in the county Kildare
And shaved before mass every Sunday.

Maggie O'Brien she said unto me
She never would marry; no never said she.
But now she is happily married to me
And the mother of seventeen children.

Tune is The Limerick Rake