Melodic ear training is the skill of listening to a musical line and recognizing the relationship of the notes to the tonal center, the key that the song is in. Does this sound like magic? We're going to cover the core of ear training in the next few minutes. After that, it's just a matter of expanding what you already know.
You are probably aware of the 4-note tune that we recognize as "How Dry I Am". The tune is the same as the hymn tune, "O Happy Day". There are many other songs that begin with these four notes, in some order. Once you get a handle on them, you'll be able to identify the most common notes that you hear.
The tune consists of a melodic "leap", and then two moves by "step", that is, they follow the major scale. The first leap consists of notes 5 and 1 of the scale, or "Sol" to "Do" if you're using solfege. This same leap, 5 to 1, occurs at the beginning of many other familiar songs. A couple of common examples are "Amazing Grace" and "Here Comes the Bride". Whenever you hear this characteristic leap, you can be sure that the second note is "Do", the tonic note.
Also interesting are the last three notes of the theme, notes 1, 2, and 3 of the scale (Do, Re, Mi). They occur often at the beginning of songs, such as "Row, Row, Row Your Boat" (with some repetitions). "Three Blind Mice" uses the same three notes in reverse order (Mi, Re, Do).
You can think of this four-note theme is several ways. You can think of it as "5, 1, 2, 3". You can think of it as "Sol Do Re Mi". Or you can even name the notes "how, dry, I, am". In any case, if you attach a particular short word to each note, it will be easier to discuss the tune. Another tune that uses the same four notes (with repetitions) is "O Christmas Tree".
One way of seeing how well you know these four notes is to see if you can recognize them in a different order. Think of the first notes of "My Bonnie Lies Over the Ocean". Same four notes, right? Can you name the order? (Here's a hint: How am I dry.) Another tune that starts with the same four notes is the verse to Jingle Bells (Dashing through the snow).
Of course, you can start on a different note of the series. Consider the tune of "I've Been Working on the Railroad". It begins on "Do", but includes the same four notes. Can you sing it on either the numbers or the syllables? (Dry how dry how dry I am dry.) And if you want to expand your range already, you can recognize that "all" of "all the livelong day" is note number 4 of the scale (Fa), a half-step higher than 3.
And for a final test, hum through the tune of the Westminster chimes, that so many clocks use when they strike the hour. These are composed of the same four notes, in different sequences. If you can sing through these correctly, on the numbers or the syllables, you probably have a good understanding of the basics of melodic ear training. Once you've tried it on your own, read on to find the answer. (3 1 2 5, 5 2 3 1, 3 2 1 5, 5 2 3 1)
You can probably hear this sequence of notes in your head in relation to many songs. Pick a number of songs at random, and you'll find that a good percentage of them use many of these notes in their main melody. And the fact that you can recognize them will make you seem like a music guru to other people.