Some ideas to get you started:

Listen to one example of the lilting you want to learn, take time to hear the different notes the singer is using, then try and sing those same notes yourself much, much slower. Keep practicing it slowly until you've got them right and then slowly speed yourself up.

Practice singing scales, major, minor, whatever mode the songs you like seem to be in. A lot of the ornaments will be within the scale. If you practice singing up and down scales and up and down thirds and fifths etc you will begin to know what your voice feels like going up and down and you can start speeding it up now and again.

Read the Threads on the Singing voice that Alice has so carefully put together, if you refresh the threads back three days you'll find that particular one. Lots of good information about singing there.

Don't wear your voice out trying to get it right in one go, smaller doses of daily practice get you a lot further without destroyiong your voice.

Have fun and experiment.