The book "Celtic Magic" by D.J. Conway is a horribly inaccurate book full of misinformation. I would personally never recommend it to anyone seeking to learn about the Celts.
The association of trees with birthdates is a modern one and there is no evidence that the Celts used this at all.
The problem with trying to learn about what the Celts did spiritually and magically is that they left no written records. The vast majority of what we know about them was passed down to us by their enemies.What you find in most books about the Celts in books in the popular press is drawn heavily from modern practices such as Wicca and would likely seem completely foreign to an ancient Celt.
Some books on the Celts that would be useful if you want to approach it from a scolarly sound basis would include:
"The Pagan Celts" by Anne Ross
"Pagan Religions of the Ancient British Isles" by Ronald Hutton
"Blood and Mistletoe" by Ronald Hutton
"Dying for the Gods" by Miranda Green
"The Druids" by Peter Berresford Ellis
And two reasonably good books on Celtic practices that I would suggest are
"The Apple Branch: A Path to Celtic Ritual" by Alexei Kondratiev
"Glamoury; Mysteries of the Celtic Green World" by Steven Blamires