You can check a dictionary for the IPA transcriptions. The difference is *huge*, but the part you're probably missing is that the vowel in "fine" is a diphthong, with a non-syllabic /i/ at the end (right before the /n/). Make sure you pronounce that little /i/. Thus, the diphthong is similar to the hanyu pinyin ai (as in 愛). Unfortunately for you, Chinese does not have this vowel followed by a nasal final, so you'll have to learn to pronounce the vowel without letting the final /n/ interfere. (Mandarin also does not have this diphthong after /f/ initial, but that's probably not your problem.) Try saying the word without the final /n/, and then add the /n/ as an afterthought. Or you may try saying it as two syllables at first (like 发音), then focusing on making the 发 much stronger and longer, and the 音 much weaker and shorter. In "fan", there is just a simple vowel, so the word is pronounced a bit like hanyu pinyin fan (as in 飯), with perhaps a bit of the sound from 言).

Fine rhymes with brine, dine, line, mine, pine, sine (wave), wine and so on. Fan rhymes with ban, can, Dan, man, pan, tan and so on. Does that help?