"to learn to know, inquire into," from Old English cunnian "to learn to know," ultimately from the same ancient root as can (v.1) and compare con (v.3). Surviving into 17c. and perhaps later in dialects. Also compare cunning.
Old English 1st & 3rd person singular present indicative of cunnan "to know," less commonly as an auxiliary, "to have power to, to be able," (also "to have carnal knowledge"), from Proto-Germanic *kunnjanan "to be mentally able, to have learned" (source also of Old Norse kenna "to become acquainted, try," Old Frisian kanna "to recognize, admit, know," German kennen "to know," Middle Dutch kennen "to know," Gothic kannjan "to make known"), from PIE root *gno- "to know."
It holds now only the third sense of "to know," that of "to know how to do something" (as opposed to "to know as a fact" and "to be acquainted with" something or someone). Also used in the sense of may, denoting mere permission. An Old English preterite-present verb, its original past participle, couth, survived only in negation (see uncouth), but compare could. The present participle has spun off with a deflected sense as cunning.
early 14c., conning, "learned, skillful, possessing knowledge," present participle of connen, cunnen "to know," from Old English cunnan (see can (v.1)), from PIE root *gno- "to know." Also compare cun (v.). Sense of "skillfully deceitful, characterized by crafty ingenuity" is probably by late 14c. Related: Cunningly.