After getting familiar with singing your Do Re Mes in your head, you'll need to put them into use.
This might sound obvious, but the key to be able to determine a melody with this is knowing the fact that every note ( Do, Re, Me, Fa, So, La, Ti, Do ), no matter how high pitched or low pitched your voice is, this sequence should always sound the same. Imagine a fully grown male adult and a dainty little girl, both singing these notes. You'll find that even though the adult male is singing in a low pitched voice while the girl is singing in a high pitch voice, somehow singing their Do Re Mes sounds very similar!
We may be using nursery rhymes as examples here but these will lay the foundation for both adults and children.
Now try to sing the following ( in your mind or out aloud) :
Me Re Do Re Me Me Me, Re Re Re, Me Me Me.
Does it ring a bell? Now try this:
Merry had a little lamb, little lamb, little lamb.
There you have it! Most simple songs can be converted into the "Do Re Me" sequence. Another classic example would be the following:
Ba Ba Black Sheep have you any wool.
Do Do So So La La La La So.
What you should try to do now is to complete these songs on your own! By turning their melodies into the Do Re Me sequence, you're actually " playing by ear".
1. Mary had a little lamb
2. Baa Baa Black Sheep
Spoiler alert
These are the corresponding notes for "Mary had a little Lamb"
Me Re Do Re Me Me Me, Re Re Re, Me Me Me.
Me Re Do Re Me Me ME, Re Re Me Re Do.
Mary had a little lamb, little lamb, little lamb
Mary had a little lamb, Its fleece was white as snow
"Baa Baa Black Sheep"
Do Do So So La La La La So, fa fa me me re re do.
So so so fa fa, me me me me re, do so so so fa fa fa fa me me me re.
Baa baa black sheep Have you any wool. yes sir yes sir three bags full
One for the master, and one for the dame, and one for the little boy Who lives down the lane.
https://www.youtube.com/watch?v=mKSaW1cm5zM
Don't worry if you're unable to decipher them on your own. What you can do is to practice singing these rhymes using " Do Re Me" until it gets familiar. The more you practice, the more fluent it gets and that helps to hard wire the notes into your head.