Are you a classical player who really loves Irish traditional music? Here are a few pointers to get started on the right foot!
1. It's "Irish", not "Celtic"
If you want to be taken seriously by trad players (that's traditional Irish players!) call it "trad", "traditional Irish" or "Irish" music, not "Celtic" music.
If "Celtic" is the best word for the situation, make sure you pronounce it with a hard C - "seltics" is a basketball team, "keltic" is the pronunciation that refers to the music of the "Celtic nations" - Ireland, Scotland, Brittany, Wales, etc. - and know that the word refers to a much bigger group than just Irish.
2. Tunes vs songs
Tunes are the pieces of instrumental music originally associated with dances. 95% of what is played in a traditional session - jigs, reels, hornpipes, polkas, barndances, etc. - are tunes. "Songs" are sung by singers - if you refer to your tunes as songs, people will likely look at you a little funny, wondering whether you know what you're talking about. Melodies from songs played on an instrument are called "slow airs".
3. It is an aural tradition
... which means that you should leave the dots at home. Even better, ignore them altogether. Look for quality recordings of the tunes you want to learn, or get them from a player you admire, and pick them up by ear. It may be slow going at first, but you'll get faster at it, and you'll immediately sound less classical.
4. Leave the vibrato at home
As a classical player, vibrato is likely an integral part of your sound. If you use air vibrato when playing Irish tunes, you'll be outed immediately as someone unfamiliar with the tradition. You might see traditional players using finger vibrato on a long note in a slow air, but as for air vibrato, leave it out.
5. Rhythm first
Trad is a dance-based genre. The tunes were originally written to be played for dancers, and as such, rhythm beats ornamentation every time. If you have to choose between adding an ornament and playing the tune in exact time, leave the ornament out.
6. Ornaments are percussive, not melodic
Ornaments in traditional music often occur where you would articulate in classical music (e.g. separating repeated notes). Because most of them have a percussive role, they should be crisp and tight, not sweeping and melodic. There are some exceptions, but if it sounds "delicate" or "pretty", you're likely being influenced by your classical ears instead of your trad sensibilities.
7. Respect the tradition
The Irish tradition is an old one, with a respected lineage, just like classical music. It has so many more levels than the notes on the page can tell you, and the biggest mistake a classical player can make (and the one mistake guaranteed to lose you friends!) is to assume you know everything about this very different, very beautiful, very vibrant and living tradition. Listen to respected players, and work to understand why they are considered by today's musicians to be the tradition bearers so you can become a living part of this tradition, too!
Be humble, listen more than you play, ask for help, and you'll be off to a great start.
Enjoy the journey!