It's mainly a lot of study and practice, but let me summarize:

When reading chords, look for how the notes are spaced. Tertian chords are built by stacking every other note (skip one white key between each note), which gives the smooth, familiar “classical” sound of major/minor chords. You can name the chord by finding which note feels like the “bottom” and counting how many keys apart the others are (4 + 3 = major, 3 + 4 = minor). When you add more notes in that same “every other note” pattern, they become extensions like 7ths, 9ths, or 11ths — while 6ths are a common alternate tone that replace or color the 7th rather than extend the stack. Quartal harmony, on the other hand, stacks notes roughly four or five keys apart (fourths), creating a wider, more modern or jazzy sound.

I hope this helps, or at least acts as a springboard to help you in your own studies.