can (v.1)
Old English 1st & 3rd person singular present indicative of cunnan "know, have power to, be able," (also "to have carnal knowledge"), from Proto-Germanic *kunnan "to be mentally able, to have learned" (cognates: Old Norse kenna "to know, make known," Old Frisian kanna "to recognize, admit," German kennen "to know," Gothic kannjan "to make known"), from PIE root *gno- (see know).

Absorbing the third sense of "to know," that of "to know how to do something" (in addition to "to know as a fact" and "to be acquainted with" something or someone). An Old English preterite-present verb, its original past participle, couth, survived only in its negation (see uncouth), but see also could. The present participle has spun off as cunning.
can (n.)
Old English canne "a cup, container," from Proto-Germanic *kanna (cognates: Old Saxon, Old Norse, Swedish kanna, Middle Dutch kanne, Dutch kan, Old High German channa, German Kanne). Probably an early borrowing from Late Latin canna "container, vessel," from Latin canna "reed," also "reed pipe, small boat;" but the sense evolution is difficult.

Modern "air-tight vessel of tinned iron" is from 1867 (can-opener is from 1877). Slang meaning "toilet" is c.1900, said to be a shortening of piss-can. Meaning "buttocks" is from c.1910.
can (v.2)
"to put up in cans," 1860, from can (n.1). Sense of "to fire an employee" is from 1905. Related: Canned; canning.