One way I have used sometimes is this: 1) decide what key you are going to sing it in. You can usually do this by trying to match the notes on the guitar to your voice. Better that way than try and my voice to a key that is out of my range. B) play just the melody on single strings of the guitar (or banjo or whatever). For simple melodies this isn't too hard if you can play the scale. III) for each important note of the melody - that is to say, each one that has an emphasis on it or lasts for very long - figure out which of the three or four chords for the song's key has that note in it. Lastly and Optionally, develop a finger-picking pattern that hits the right notes in the chords at the right rhythmic moments. This will often involve adding/subtracting notes from the chord at certain points.

I've learned a good oh, four or five songs this way ;) FWIW