late 14c., in Bible translations, the Hebrew word shibboleth, meaning "flood, stream," also "ear of corn," as used in Judges xii.4-6. During the slaughter at the fords of Jordan, the Gileadites took it as a password to distinguish their men from fleeing Ephraimites, because Ephraimites could not pronounce the -sh- sound. (Modern commentators have decided the Hebrew word there probably was used in the "river" sense, in reference to the Jordan).
Hence the figurative sense of "watchword or test-word or pet phrase of a party, sect, school, etc." (by 1630s), which evolved by 1862 to "outmoded slogan still adhered to."
Elsewhere in history, a similar test-word was cicera "chick pease," used by the Italians to identify the French (who could not pronounce it correctly) during the massacre called the Sicilian Vespers (1282). There have been, and will be, others.
During training exercises on Pavuvu and Guadalcanal, the need to improve battlefield security is to be implemented not by a simple password, but by an identification procedure described as "sign and countersign." The ground rules are to sequentially interrogate an unknown friend or foe with the name of an automobile, preferably one with an "L" in its vocalization. The response is to be a cognomen for another automobile uttered in the same manner. This insures the "friend" entering our lines will reply with the correct countersign in a dialect distinctly American; call out "Cadiwac" or "Chryswer," and you're dead. [Perry Pollins, "Tales of a Feather Merchant: The World War II Memoir of a Marine Radioman," 2006]
Middle English seien, from Old English secgan "to utter, inform, speak, tell, relate," from Proto-Germanic *sagjanan "to say" (source also of Old Saxon seggian, Old Norse segja, Danish sige, Old Frisian sedsa, Middle Dutch segghen, Dutch zeggen, Old High German sagen, German sagen "to say").
Watkins has this from a PIE *sokwyo-, from a root *sekw- (3) "to say, utter" (source also of Hittite shakiya- "to declare," Lithuanian sakyti "to say," Old Church Slavonic sociti "to vindicate, show," Old Irish insce "speech," Old Latin inseque "to tell say"). Some further see this as identical to the PIE root *sekw- (1) "to follow" (with semantic development to "see" and then "speak"). But others doubt it and Boutkan gives it "No certain PIE etymology."
The past tense form said developed from Old English segde. Impersonal use (it is said) was in Old English. The notion in shall we say, etc. (1580s) is "suppose, take for granted." On that analogy, impersonal say is used as an introduction word, or parenthetically, with a clause and meaning "suppose, assume" (c. 1600). Its colloquial use as an expression of surprise, etc. is by 1830.
Not attested before 1930 in use with inanimate objects (clocks, signs, etc.) as subjects. You said it! "you're right" is attested by 1919; you can say that again as a phrase expressing agreement is by 1925, American English colloquial. You don't say(so) as an expression of astonishment (often ironic) is attested by 1779. The Society of American Florists' advertising slogan say it with flowers dates to 1918 from it grew other say it with constructions.