I own an antique store and found a canapé plate of a bar scene and two gentlemen toasting. The words under the scene are "Here's How!" What is the country of origin? This plate is dated 1933 from a series of international toasting scenes.
The toast was popular enough in the US in 1917 to inspire this little ditty in prohibitionist literature. From Temperance: A Monthly Journal of the Church Temperance Society, Volume 9 (Vol. IX. No. 5, January 1917)
To wreck a fine career,
To make all pleasure cost you dear,
To fill each day with grief and fear!
To lead a useless life,
To break the hear of child or wife,
To give the home to bitter strife!
You find the down-hill road,
Under an ever-stinging goad;
Here's how the crop of ruin's sowed!
The devil wins the game;
Whate'er the start, the ends's the same
Drink deep - it costs hearth, wealth and fame!
Published almost exactly two years before these fanatics got their way, and the US embarked on its almost entirely successful campaign to stop the scourge of hard liquor by outlawing it,
Leslie Dunkling, The Guinness Drinking Companion (2003), in a subsection titled "Fictional Formulae," has this remark about toasts offered in fictional works:
I have noted a few other examples while working on this book. They include chin chin! cheerio! (together with cherry-oh!) here's luck! here's to you! skin off your nose! here's how! down the gully! here's lead in your pencil! here's looking up your kilt! here's mud in your eye! bottoms up! down the hatch! bung-ho! up yours! Someone somewhere, must have a full collection of such terms, but I have yet to see it.
From this list it appears that "Here's how!" may have been common in unspecified parts of the English-speaking world—perhaps in multiple places. For the record, I advise against saluting a fellow drinker, at least in the United States, with the toast "Up yours!"
Jonathon Green, Cassell's Dictionary of Slang (2005) offers this entry for the phrase:
here's how! excl. [20C+] a popular toast before drinking.
And Eric Partridge, Dictionary of Slang and Unconventional English, first edition (1937), has this:
here's how ! A late C. 19–20 coll[oquial] toast. ? used before Kipling, 1896, in Seven Seas.
The reference to Kipling is to a poem called "The Lost Legion," dated 1895, reprinted in The Seven Seas (1896), which ends with these lines:
Yes, a health to ourselves ere we scatter,
For the steamer won't wait for the train,
And the Legion that never was 'listed
Goes back into quarters again!
Goes back under canvas again.
The swag and the billy again.
The trail and the packhorse again.
The trek and the lager again.
This certainly suggests a British Isles origin of the toast, and I haven't heard it used in the United States, though whether it once was is quite another question.
A further discussion appears in Eric Partridge, A Dictionary of Catch Phrases, American & British, From the Sixteenth Century to the Present Day, second edition (1992):
here's how!, by itself is ineligible, for it's a mere drinking conventionalism. It has, however, prompted the elab[oration]:
here's how! I don't mean 'how'; I mean 'when'. I know how. A correspondent from Highworth, Wiltshire, mentions having heard it in 1944. And A.B., from the US, 1978, adds, '"I know how — who is the problem": since c. 1950s.'
This account suggests that "Here's how" was used on both sides of the Atlantic by the 1950s.