Here is a method that I use to figure out a melody in my head, without an instrument.

For example. Lets say we want to learn the melody to "fool on the Hill". We can all think of the melody playing, note by note. So how do we learn what those notes are?

As I hear each note of the melody, I think of another tone, which is the key of the song. So the current melody note and the root of the song create an interval. If you are able to identify what interval that is, the you know what the melody note is, and you can then move to the next note.

For example, as I hear the first note of fool on the hill, and the compare it to the root, I know that the interval is a major 3rd, and that the first note of the song is the major 3rd of the scale. If the song was in F, that why mean an A note.

So if you want to try it, sing the melody, but after every note, sing the key of the song too.
If it works, you should be able to figure out the melody of Happy Birthday in your head, without even knowing what key you are in, just remembering the scale tones relative to the song key.

I've never taken a sight singing class, and that's likely the type of thing that they teach you on the first day!

Have Fun!
Peter Gannon
PG Music Inc.