Part of it is just practice and familiarity. As you sing tunes you are familiar with, watch that highest line of notes (almost always the melody) as it goes up and down and get a feel for how going from low to high feels, or just a small step feels.
Also, it's very helpful to familiarize yourself with how long notes should last. The vertical lines you see in music are a "measure" and you might think of that like a musical paragraph. Each measure will have the same number of beats, but you could have 1 or a half dozen notes making up that beat. Here is an example:
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A whole note (with no staff attached to it) lasts the entire measure, in this case four beats. Two half notes (open but with staffs) will take up the entire measure (four beats). Four quarter notes (black with a staff) will take up the entire measure (four beats with one beat each). A dot adds half again to the note's value (a half note has two beats so a dot next to a half note makes it 3 beats).
And they can be combined, so for example you could put one half note and two quarter notes together to fill out the measure with four beats. Familiarizing yourself with this will give you a sense of timing.
I think just understanding the basics will get you a very long way, you don't need a lot of music theory. Learn the relative length of various notes, get a feel of how much up or down a note goes, and practice.
The basic explanations found in this set of videos is very helpful in my mind (it's a series on playing the Ocarina but gives an excellent introduction to basic reading of music):