Before starting to play, you need to ask yourself two good questions:
Which kind of tune is it ? jig, reel, hornpipe... ? it will define the rhythm.
Which mode and keys ? major, minor, mixolydian, dorian ? D, G...?
it will define your chords agreements.
To get an easy answer to the second question, there are general agreements to the mode.
Like II - V - I for jazz music, it would make for Irish music :
-Ionian: I - I - IV - V
For example in D aeolian (major) : D - D - G - A
- Mixolydian: I - I - VII - IV
For example in D mixolydian : D - D - C - G
- Aeolian: Im - Im - VII - Vm
For example in D ionian (minor) : Dm - Dm - C - Am
- Dorian: Im - IV - VII - Vm
For example in D dorian: Dm - G - C - Am
Be careful, these are general agreements, there are a lot of exceptions and "false friends". If you know the melody before to play the chords, it will help you !