1740, "in any way or manner," from any + how (adv.). Unlike most other any + (interrogative) compounds, there is no record of it in Old or Middle English. Compare anyway (16c.). Also used as a conjunction, "in any case." Emphatic form any old how is recorded from 1900, American English.
Entries linking to anyhow
"one, a or an, some," Old English ænig (adjective, pronoun) "any, anyone," literally "one-y," from Proto-Germanic *ainagas (source also of Old Saxon enig, Old Norse einigr, Old Frisian enich, Dutch enig, German einig), from PIE root *oi-no- "one, unique." The -y may have diminutive force here.
As a noun, late 12c.; as an adverb, "in any degree," c. 1400. Emphatic form any old______ (British variant: any bloody ______) is recorded from 1896. At any rate is recorded from 1847. Among the large family of compounds beginning with any-, anykyn "any kind" (c. 1300) did not survive, and Anywhen (1831) is rarely used, but OED calls it "common in Southern [English] dialects."
[A]ani refers to single entities, amounts, etc., occurring at random or chosen at random, as being convenient, suitable, to one's liking, etc. It is frequently emphatic and generalizing, having the force of 'any whatever, any at all' and 'any and every'. It is common in questions, conditional clauses, and negative statements, but not in affirmative statements (where som is used instead). [The Middle English Compendium]
How come? for "why?" is recorded from 1848 [Bartlett]. Emphatic phrase and how! is recorded from 1865. The formulation was common in book and article titles ("The National Debt, and How to Pay It"), but Pennsylvania writer Bayard Taylor, in whom it is first recorded, seems to have regarded it as a German or German-American expression.
Middle English in this sense had ani-gates "in any way, somehow" (c. 1400), also on anikinnes wise "in any way or manner" (c. 1200), and Late Old English had on enige wisan "in any wise, in any manner." As a prepositional phrase, in any way is from late 14c.
they came anyhow they could