The next chords can be harmonised by Ib-IV. The B drops a 3rd to G sharp so the obvious choice of chord is IIb which follows nicely to the interrupted cadence. The D is a passing note so the chords would be Vb to I. We now have the following incomplete sketch: Taking into account what follow an interrupted cadence would be best (V-VI).
Bars 1-2 – The melody being leading note to tonic must be either an interrupted or inverted perfect cadence.The obvious cadences are in bars 1 to 2, 4 and 7 to 8. To begin harmonizing this melody we must see which chords are available to us: Consider picking up Harmony and Theory: Essential Concepts Series if you want the definitive comprehensive guide.