The harmonies generally will transcribe from what happens on piano to other instruments. If the harmony in a particular bar is around an F# chord, then all the instruments will need to be playing mainly the notes F# A# and C#. Not necessarily at the same time, but maybe the clarinet for example, could play A# and C# in that bar, half and half, while the trumpet plays F# G# and A#.
Look at it all vertically, bar by bar, checking that the main notes contained therein mostly constitute the underlying chord, as indicated in the original piano accompaniment.
Arranging a song is far more complex, with different mixes of instruments, coming in and going out, but that question is hinted at in the question as posed. It's another one for another day.