John and Caitlin Mathews have done a really great job on writing about the Celtic peoples. You should check them out. Also look into Oak, Ash, and Thorn.
Yes, what Tom said. I would recommend starting by reading the mythology of the particular Celtic branch that interests you. Irish and Welsh probably have the most written material available (though it's mostly second-hand, written down by Christian scholars, it's still quite valuable as a resource).
The problem with Celtic paganism is pre-Christian Celts didn't write much down and also "Celtic" covers a large disperse group. There is no practice that has existed in an unbroken line back to early Celtic pagans.
Here's a good site to get some basics.
Celtic Reconstructionism is the term used for those trying to follow a path true to the old religions.
I study Druidism but modern Druidry, also called Neo-Druidry, is mostly from the 18th century or later.
There are plenty of good books on Celtic history and mythology but they don't in themselves make a religion you can practice.