I imagine you are vaguely familiar with subtractive synthesis; oscillators, filters, envelopes, modulation. It wouldn't hurt, although the building blocks are laid out differently in an FM synth.

Anyway, I found these hands-on demos on the DX1 to be some of the most "aha" moments I've had trying to understand how FM patches are made.

TLDR, an FM "operator" is an oscillator. A carrier is the oscillator you hear, its modulator is an oscillator that wiggles the carrier and brings out different harmonics. You can stack more modulators and you can have multiple carriers going in parallel, the various combinations of operators available in a synth being the different algorithms.

https://www.youtube.com/watch?v=YV9vQGqoO5c

https://www.youtube.com/watch?v=k0xGyR_lKoM

https://www.youtube.com/watch?v=1-boGIxRZ_s

There was also one from Venus Theory about how to get musically useful stuff out of frequency/phase modulation: https://www.youtube.com/watch?v=wqc8rZnzTVI