Every interval below starts on the same note, so you can see the shape change.
The rule: odd-numbered intervals sit on the same kind of place: both on lines, or both in spaces. Even-numbered intervals straddle: one on a line, one in a space.
Both noteheads on lines (or both in spaces). Count the gap: adjacent = 3rd, skip one = 5th, skip two = 7th.
One notehead on a line, the other in a space.
How to use this: check the shape first (same kind or straddling) and you've halved the possibilities before thinking about size. Then judge the gap. Learn 2nds, 3rds and the octave first; they're the most common and the easiest to spot.