Old English be- (unstressed) or bi (stressed) "near, in, by, during, about," from Proto-Germanic *bi "around, about," in compounds often merely intensive (source also of Old Saxon and Old Frisian bi "by, near," Middle Dutch bie, Dutch bij, German bei "by, at, near," Gothic bi "about"), from PIE *bhi, reduced form of root *ambhi- "around."
As an adverb by c. 1300, "near, close at hand."
OED (2nd ed. print) has 38 distinct definitions of it as a preposition. Originally an adverbial particle of place, which sense survives in place names (Whitby, Grimsby, etc., also compare rudesby). Elliptical use for "secondary course" was in Old English (opposed to main, as in byway, also compare by-blow "illegitimate child," 1590s, Middle English loteby "a concubine," from obsolete lote "to lurk, lie hidden"). This also is the sense of the second by in the phrase by the by (1610s).
By the way literally means "along the way" (c. 1200), hence "in passing by," used figuratively to introduce a tangential observation ("incidentally") by 1540s. To swear by something or someone is in Old English, perhaps originally "in the presence of." Phrase by and by (early 14c.) originally meant "one by one," with by apparently denoting succession; modern sense of "before long" is from 1520s.
By and large "in all its length and breadth" (1660s) originally was nautical, "sailing to the wind and off it," hence "in one direction then another;" from nautical expression large wind, one that crosses the ship's line in a favorable direction.
c. 1200, from Old Norse geta (past tense gatum, past participle getenn) "to obtain, reach; to be able to; to beget; to learn; to be pleased with," a word of very broad meaning, often used almost as an auxilliary verb, also frequently in phrases (such as geta rett "to guess right"). This is from Proto-Germanic *getan (source also of Old Swedish gissa "to guess," literally "to try to get"), from PIE root *ghend- "to seize, take."
Old English, as well as Dutch and Frisian, had the verb almost exclusively in compounds (such as begietan, "to beget;" forgietan "to forget"). Vestiges of an Old English cognate *gietan remain obliquely in modern past participle gotten and original past tense gat, also Biblical begat.
In compound phrases with have and had it is grammatically redundant, but often usefully indicates possession, obligation, or necessity, or gives emphasis. The word and phrases built on it take up 29 columns in the OED 2nd edition; Century Dictionary lists seven distinct senses for to get up.
"I GOT on Horseback within ten Minutes after I received your Letter. When I GOT to Canterbury I GOT a Chaise for Town. But I GOT wet through before I GOT to Canterbury, and I HAVE GOT such a Cold as I shall not be able to GET rid of in a Hurry. I GOT to the Treasury about Noon, but first of all I GOT shaved and drest. I soon GOT into the Secret of GETTING a Memorial before the Board, but I could not GET an Answer then, however I GOT Intelligence from the Messenger that I should most likely GET one the next Morning. As soon as I GOT back to my Inn, I GOT my Supper, and GOT to Bed, it was not long before I GOT to Sleep. When I GOT up in the Morning, I GOT my Breakfast, and then GOT myself drest, that I might GET out in Time to GET an Answer to my Memorial. As soon as I GOT it, I GOT into the Chaise, and GOT to Canterbury by three: and about Tea Time, I GOT Home. I HAVE GOT No thing particular for you, and so Adieu." [Philip Withers, "Aristarchus, or the Principles of Composition," London, 1789, illustrating the widespread use of the verb in Modern English]
As a command to "go, be off" by 1864, American English. Meaning "to seize mentally, grasp" is from 1892. Get wind of "become acquainted with" is from 1840, from earlier to get wind "to get out, become known" (1722). To get drunk is from 1660s; to get religion is from 1772; to get better "recover health" is from 1776. To get ready "prepare oneself" is from 1890; to get going "begin, start doing something" is by 1869 in American English; get busy "go into action, begin operation" is from 1904. Get lost as a command to go away is by 1947. To get ahead "make progress" is from 1807. To get to (someone) "vex, fret, obsess" is by 1961, American English (get alone as "to puzzle, trouble, annoy" is by 1867, American English). 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 horsemanship. To get on (someone's) nerves is attested by 1970.