If you are able (musically experienced) to sing the bassline to a given melody you will easily find the fitting chords and very often you‘ll find several solutions. Start playing „this old house“house of rocky docky“, joyful, joyful, „silent night“. go by googlesearch: songtitle and chords"chords", and by practice your analytic ear will get trained. most songs can be accompained with tonica, dominante subdominante, in your case D.G and A7. many songs have a dominante of the dominante (V/V) in the half-end, that means before the repetition of the first line. there are a few patterns of chord progressions to accompain almost all songs: the best way to find the right chords is to get skilled in playing following chord progression using the circle of fifths: I-V-I tonica dominante tonica I-V V-I I-IV-V-I "cadence" I-V-V-I; IV-I-V-I (the mozart scheme) then the well known 12 bar blues scheme and the sub-dominante cadence (jazz cadence) I-I7-IV-IVm-I-V-I (e.g. oh when the saints go marchin' in) most popular: many pop songs have the following cadence I-VIm-IIm-V7 and some variations of this ... with a lot of practice of it you will learn to find out the right chords! concerning joy to the world: this is just very special and difficult .. as it is a barock tune of handel: try to find the right bass line (think of counterpoint) as the melody goes down you try to sing a bass line that goes up and try to accompaigne the scale do re mi fa ... up and down.
