There are two ways to understand intervals: the right way, and the way I learned them. Before we get into that, let me point you to some good resources for learning the right way. I like the online tutorials by Robert Hutchinson, Chelsey Hamm and Bryn Hughes, musictheory.net and musicca.com. I really love Nate May's visual approach. And if you like learning from videos (which I don't), this one by Saher Galt is good. I find it most helpful to visualize the intervallic structure of the diatonic scale on a circle, and if you like to think that way too, try the aQWERTYon.
I am an aural learner who needs concrete examples, so I made this track for my students to sing along with in class, and for practice outside of it. It combines a soothing tanpura drone with the Apache break. Here's an interactive Noteflight score.
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