I have a song in 6/8 that has 4 dotted eighth notes in the treble clef with no rests. On what beat does each note play? I cannot figure this out for some reason.
This is an example of a 2-against-3 cross rhythm. A more intuitive way of notating it, and one that helps you perform it, would be:
You'll note that each value comprises an eighth and a sixteenth; this is why your notation just has four straight dotted eighths.
In order to practice this rhythm, you might start out by removing the ties in my notation. This way, you're playing 1 2&3 4 5&6. Once you're really comfortable with this pattern, add in the ties so that you're only playing 1 ~&~ 4 ~&~.
As you become more fluent with this, you'll notice that you're playing two articulations per large beat. This is why we call this a 2-against-3 cross rhythm: you're playing two pitches per three written eighth notes. Because of this duple feel within a triple rhythm, you'll sometimes see it notated as duplets:
All three notations (including yours) are of the same rhythmic profile.