I'm assuming that most people will be reading myths from a book. However, we must learn to listen to them, to give them our deep attention. There are definite advantages to hearing someone tell stories from Celtic mythology in person, especially if the speaker is pronouncing the names in their native language. (Wrong pronunciations can be hard to unlearn so it's great to hear correct ones early on.) There is an immediacy and a shared experience with live storytelling that no other method has. Listening to recordings can also be good, but it can be harder to keep your full attention on a recording. However, an advantage that both books and recordings have, is that you can go back over things whenever you want to. The "listening" I'm talking about, though, is not about reading vs hearing, but about how we receive and respond to the story once we encounter it.
As you read mythology you will probably encounter events, statements or ideas that cause a strong response. Your response might be awe or aversion, an epiphany or downright puzzlement. A good storyteller knows these points in a tale, and will pause, perhaps even repeat a phrase, or explain something. When we read myth, we act as both teller and listener, so please show honour to both yourself and the story by sitting for a moment to feel or think, or even going back over something that stands out.
Over time, some myths will probably feel more important to you than others. Remember that in a storytelling culture, an individual will hear the same stories many times in their life. Allow the tales that are important to you to get under your skin. Allow yourself to live and eat with them, to dream them. As well as reading my favourites often, maybe in different translations, I sometimes try to repeat them in my mind, as if I was telling them to a group of friends. This allows me to see how well I know the story. Can I get all the events in the right order? Am I clear on any causes and effects? This is a great way to make the story part of your life, and maybe one day you will find yourself telling it.
I often hear people encouraging those new to the Celtic path to read various books about mythology "for starters". While they often suggest very good books, I feel that you should let the myths themselves have their say first. Keep an open mind. At some point you may want to read commentary on the myths that interest you. You may be questioning your own interpretation, or just want to learn more about them. There is much depth to be found this way, but the depth you find on your own is real, too. It can be both magical and fragile. Don't let a more scholarly interpretation crush the wisdom you've found. Maybe your wisdom will evolve, and maybe the scholars' wisdom is not the only wisdom.
Celtic mythology is hard to pin down. It's messy, fragmented and mysterious. You have to work for what you get out of it. Talking about mythology is not the same thing as listening to it. If you do listen, you'll find that somehow the gods have woven themselves into the strands of it in such a way that if you look for them there, or you look for wisdom or 'medicine' there, they will meet you halfway. They will meet you with things that are relevent to you right now.
"In this tradition a story is 'holy,' and it is used as medicine ... The story is not told to lift you up, to make you feel better, or to entertain you, although all those things can be true. The story is meant to take the spirit into a descent to find something that is lost or missing and to bring it back to consciousness again."