c.1200, from Old Norse geta "to obtain, reach; to beget; to guess right" (past tense gatum, past participle getenn), from Proto-Germanic *getan (cf. Old Swedish gissa "to guess," literally "to try to get"), from PIE root *ghend- "seize, take" (cf. Greek khandanein "to hold, contain," Lithuanian godetis "be eager," second element in Latin prehendere "to grasp, seize," Welsh gannu "to hold, contain," Old Church Slavonic gadati "to guess, suppose"). Meaning "to seize mentally, grasp" is from 1892.
Old English, as well as Dutch and Frisian, had the root only in compounds (e.g. begietan "to beget," see beget; forgietan "to forget," see forget). Vestiges of Old English cognate *gietan remain obliquely in past participle gotten and original past tense gat. The word and phrases built on it take up 29 columns in the OED 2nd edition. Related: Getting.
Get wind of "become acquainted with" is from 1840, from earlier to get wind "to get out, become known" (1722). Get out, as a command to go away, is from 1711. Get-rich-quick (adj.) attested from 1904, first in O. Henry. To get out of hand originally (1765) meant "to advance beyond the need for guidance;" sense of "to break free, run wild" is from 1892, from horses. To get on (someone's) nerves is attested by 1970.