"The Parting Glass" is a wonderful song about reconciling with the past, feeling the sadness of endings and partings, and doing what people love to do at such times: drink! I was pleasantly surprised to note the similarity of this song to an early Dylan song "Restless Farewell". 

We use a simple accompaniement pattern: playing the root of the chord with the thumb, followed by 3 picked notes with fingers index, middle, ring (which will play only the top 3 strings each time, so the thumb will change, but the fingers will not). In The Principles, this is known as "the 4 note arpeggio", a fundamental right hand technique which is mastered by doing the "finger dipping exercises" to establish true independent control of each finger.

VERY IMPORTANT: Be aware of tension going into the thumb when you use the fingers. It will tend to make the thumb move AWAY from the strings, which is not where we want it. Follow the thumb.

 Also, I would suggest using the full F bar chord for a better sound. If you have trouble with this chord, read "Easy Bar Chords".