Let’s learn the verb “learn,” because it seems appropriate.
We are going with “learn” here in the sense of acquiring new knowledge or skills by study, not “learn” in the sense of “found out,” like “I just learned that your moose dented my car!” They are different concepts and translate differently.
“Learn” can be translated two different ways: آموختَن (āmūkhtan, present stem آموز āmūz) or یاد گِرِفتَن (yād giriftan, present stem یاد گیر yād gīr). The latter literally means “to take a memory,” so it can work either in terms of classroom learning or sort of picking up a bit of trivia, but the former mostly carries the sense of formal learning. The complication, because obviously there must be one, is that آموختَن can also mean “teach” (the corresponding alternative is یاد دادَن yād dādan, “to give a memory”), so context is crucial.
“I am learning Persian” = زَبانِ فارسی را می آموزَم (zabān-i fārsī rā mī āmūzam) OR زَبانِ فارسی را یاد می گیرَم (zabān-i fārsī rā yād mī gīram)
“Yesterday they learned the names of the planets” = دیروز نامهای سیارات را آموختَند (dīrūz nāmhā-yi siyārāt rā āmūkhtand) OR دیروز نامهای سیارات را یاد گِرِفتَند (dīrūz nāmhā-yi siyārāt rā yād giriftand)
“Education” = آموزِش وَ پَروَرِش (āmūzish va parvarish, “aa-moo-zesho-par-var-esh,” lit. “teaching and training”). Also be aware of تَحصیل (taḥṣīl), from the Arabic verb for “acquire” but in Persian meaning “schooling” or “studies.”
“Student” = دانِش آموز (dānish-āmūz, lit. “knowledge learner,” generally used for elementary-secondary students and not for college students, who are instead called دانشجو dānishjū)