Here’s the IPA. “Plain” and “plane” are both /plein/. The “ei” has the same value as in Hanyu Pinyin — just add /n/ to the end for /plein/. This can be difficult for some Mandarin speakers, but actually you’re already saying it correctly. “Plan” is theoretically /plæn/. The /æ/ is a vowel between /e/ and /a/. It’s similar to the “a” in Hanyu Pinyin “yuan”. In general American accent, however, /æ/ is usually pronounced as a falling diphthong when followed by /n/ or /m/ (but not /ŋ/). In this case the pronunciation is really /pleən/. To do this, start out the same as for /ei/, but instead of gliding to /i/, we glide to the schwa /ə/. The schwa is similar in quality to Hanyu Pinyin “e” in the neutral tone, as in the usual pronunciation of 呢 or 的. So “plane” starts out /ple/ and then a quick, soft, toneless Hanyu Pinyin “yin”. “Plan” starts the same (/ple/), but then ends with a quick, soft, toneless Hanyu Pinyin “en”.

Plane rhymes with main, bane, sane, feign, cane, rain, Dane, gain, Jane, lane, pane, wain. Plan rhymes with bran, can, Dan, fan, LAN, man, naan, pan, ran, Stan, tan, van. You might as well practice all these words at the same time!

Plane sounds the same as the word plain. Plan sounds like LAN with a "p" at the beginning, if you know what this is (LAN is the acronym for local area network). So, try thinking of it like pLAN. In truth, both words sound very different to me! Good luck!