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 !