I play mountain dulcimer. Naemanson, you say your left hand has two usable fingers. You may be able to play chords if you tune it D A A. This tuning has a simple chord pattern. For most chords, you put your index finger on the melody note and another finger, usually the middle finger on the D string, one fret behind the melody. Strum or finger all three strings and you will have a chord.

The right book or site should fill you in on the exceptions.