It's a matter here of learning by observation (βλέπειν, ὁρᾶν, ἰδεῖν) or acquiring information by the grapevin (ἀκούειν).
For the latter, see L&N, §35.212:
33.212 ἀκούωc: to receive information about something, normally by word of mouth — ‘to receive news, to hear.’ ἀκούσαντες οἱ μαθηταὶ αὐτοῦ ἦλθον καὶ ἦραν τὸ πτῶμα αὐτοῦ ‘when his disciples received news about this, they came and got his body’ Mk 6:29. In Mk 6:29 ἀκούω clearly implies more than mere physiological hearing, for the content of the message is included as a significant element in the meaning of ἀκούωc. Compare also ἀκοήd (33.213).
For the former, see L&N §27.5
27.5 ὁράωf; συνοράωa: to acquire information, with focus upon the event of perception — ‘to learn about, to find out about.’
ὁράωf: ἐραύνησον καὶ ἴδε ὅτι ἐκ τῆς Γαλιλαίας προφήτης οὐκ ἐγείρεται ‘search and learn that from Galilee no prophet ever arises’ Jn 7:52.
συνοράωa: συνιδόντες κατέφυγον εἰς τὰς πόλεις τῆς Λυκαονίας ‘when they learned about it, they fled to cities in Lycaonia’ Ac 14:6.
Louw & Nida is really a very good resource for matters like this; one tends to forget about it because it's more like a thesaurus than a dictionary. But that's the function of a thesaurus, to clarify the nuances and precise usages of worrds that are similar. Beginners may not find L&N very useful, but anyone seeking to move to a better grasp of the Koine of the GNT will find this a very valuable resource.