Considering that Webster published his first dictionary in 1806, is there a recognised tipping point (year, decade, etc.) that marked the move from traditional British spelling to Webster's American? Was this shift a gradual but chaotic process or was it a deliberate and possibly collective decision taken by the educational institutions, the media, or the government of the time? In other words, how did the shift come about?
The answers to your questions are:
Yes, there were a few changes that Webster tried, but the history of English spelling is much, much, much more complicated than that. English has never had a single agreed-upon spelling, even within any one country. There is no such thing as the American spelling, nor for that matter is there the British spelling, when discussing the English language. At most, there are individual words that may show a general predilection, but that shifts over time and within writers and publishers. It isn’t a simple us-vs-them situation almost in any pairing. There is too much historical variation.
Here is a summary of my findings below sorted by year:
There is a lot more variation than even that summary shows; please see the more detailed charts below, including some that go the other way by showing British usage. Each of these really is a separate case, and must be considered individually. There is no single, solitary, discrete, and agreed-upon thing called American spelling versus British spelling. There is a vast continuum of conflicting tendencies, some weaving back and forth time across the Atlantic, and across time. Even when one spelling “supersedes” another, it merely comes out ahead in the popularity contest. It usually does not wholly supplant the former spelling.
For the Ngramaniacs
In all cases, the putative “American” spelling is in blue, and the putative “British” spelling is in red. Notice how the answers are all over the board, and some rather surprising, too.
center vs centre
When did center supersede centre in American English? Answer: Around 1910. Ngram
theater vs theatre
When did theater supersede theatre in American English. Answer: During the late 1970s. Ngram
armor vs armour
When did armor supersede armour in American English? Answer: Around 1850. Ngram
glamor vs glamour
When did glamor supersede glamour in American English? Answer: Never, because it has always been a minority usage. Ngram
woolen vs woollen
When did woolen supersede woollen in American English? Answer: around 1905. Ngram
tire vs tyre
When did tire supersede tyre in American English? Answer: Never, because it was always dominant. Ngram
Well, and when did tyre supersede tire in British English? Answer: in the early 1940s. But it only lasted a couple of decades before falling back into minority usage again. Ngram
miter vs mitre
When did miter supersede mitre in American English? Answer: Around 1920. Then again around 1940. Then again around 1970. Ngram
acknowledgment vs acknowledgement
When did acknowledgment supersede acknowledgement in American English? Never. It has always been that way. Ngram
What about the other way around? When did acknowledgement supersede acknowledgment in British English? Answer: Around 1970. Ngram
scepter vs sceptre
When did scepter supersede sceptre in American English? Answer: Around 1980. Ngram
savior vs saviour
When did savior supersede savior in American English? Answer: Around 1930. Ngram
deputize vs deputise
When did deputize supersede deputise in American English? Answer: Around 1810. Ngram
But what about the other way around? When did deputise supersede deputize in British English? It’s arguable, but the general answer is that it never did. Ngram
ameba vs amoeba
When did ameba supersede amoeba in American English? Answer: Never. Ngram
jewelry vs jewellery
When did jewelry supersede jewellery in American English? Answer: Around 1810. Ngram
connection vs connexion
When did connection supersede connexion in American English? Answer: Around 1845. Ngram
But what about the other way around? When did connexion supersede connection in British English? Answer: Around 1820. But it only did so for around 30 years, up through around 1850. Ngram
colored vs coloured
Since this one seems to be everybody’s favorite peeve, when did colored supersede coloured in American English? Answer: Around 1840. Ngram
leveled vs levelled
When did leveled supersede levelled in American English? Answer: Around 1915. Ngram
fetus vs foetus
When did fetus supersede foetus in American English? Answer: around 1910. Ngram
Hm, but what about the other way around? When did foetus supersede fetus in British English? It didn’t: it gave up the lead around 1970. Ngram
paralyzed vs paralysed
When did paralyzed supersede paralysed in American English? Answer: Always. ngram
And the other way around: when did paralysed supersede paralyzed in British English? Answer, around 1830, but it has been losing a lot of ground recently. Ngram
specter vs spectre
When did specter supersede spectre in American English? Answer: around 1940. Ngram
esophagus vs oesophagus
When did esophagus replace oesophagus in American English? Answer: Around 1910. Ngram
But what about British usage? The answer is that oesophagus seems to have lost to esophagus around 1980, but then may have returned. It’s hard to tell. Ngram
aluminum vs aluminium
When did aluminum supersede aluminium in American English? Answer: around 1900. Ngram
And what about the other way around? When did aluminium supersede aluminum in British English? Answer: around 1850, but it has lost a great deal of ground of late. Ngram
surprize vs surprise
It turns out that surprize was once the dominant form, not surprise, but this didn’t last even a hundred years. Ngram
Then again, here is the British Ngram for the same pair. Notice that even the Brits used the z for a good while, possibly even for longer than in North America:
I hope you can now see why I said what I said: that there can be no clear answer here. Everything is different. You have to look at each word-pair separately, and you should make sure you aren’t wrong about Britain, either.
While the progress of English spelling reform (which is apparently the term of choice) in the United States generally appears to have been gradual and chaotic, three major periods of change through deliberate process seem to be its primary drivers.
Webster's first dictionary, A Compendious Dictionary of the English Language, was published in 1806. He then spent twenty years revising it to produce the first American Dictionary of the English Language (ADEL) which was published in 1828. An expanded and revised second edition appeared in 1841. Although it drew some protest, the reformed spellings were gradually adopted throughout the United States.
While Webster championed a number of spelling reforms, only a few were widely adopted.
The release and adoption of the ADEL editions certainly corroborates with a number of ngrams which show the new American spelling steadily becoming popular after the 1820s and eventually becoming more dominant on or after 1845. For example,
There are a number of other similar instances. There are also examples such as fraternize vs. fraternise where the former, while already (in terms of the ngram) maintaining a small lead in preference, takes a sudden leap after ~1835.
As mentioned earlier, only a few of Webster's reforms, of which many were contentious, were adopted. After his death, the more egregious of his changes were gradually dropped by subsequent editors. In the 1870s, the American Spelling Reform Association was formed. They, along with the American Philological Society and the American Philological Association worked further on simplifying (American) English spelling.
We can see the effect of these reforms via a couple of ngrams:
1906 saw the formation of the American Spelling Board which was funded by Andrew Carnegie. They published a list of 300 words which were adopted by President Roosevelt for government use.
The effect of these reforms can be seen in the following ngrams:
To summarise, the divergence of American spelling is the result of spelling reforms initiated by Webster, taken further by interested parties including at least one media house, and eventually, the (temporary) backing of the US government. However, only a small percentage of each set of proposed reforms were adopted at any one time. The more drastic of reforms met with stiff resistance:
Oesophagus has always been spelt that way in Britain. If spelt correctly, Tyre and tire are two entirely different words, as has already been pointed out. I have never seen foetus spelt as fetus in the UK. Paralysed is always the correct spelling here and aluminium is always aluminium.
I am a bit puzzled about where some of the data on 'British English' is coming from, as it is very suspect.
One needs to understand that a lot of this has to do with the advancing tide of universal public education in the US. Some public schools were developed in the mid to late 1700s (Benjamin Franklin had a hand in starting one), but the movement really gained steam in the early 1800s. (Horace Mann was a well-known advocate, and, as a result, has nearly as many schools named after him as Washington or Lincoln.) Education came to be seen as not only a legitimate concern of state and local governments, but in many cases one of the most important aspects.
The resulting explosion in public schools, especially at the elementary level, was so vast (as was the westward migration of the population) that most school teachers had an eighth-grade education, often considerably less. As a result they relied on what was essentially a prescriptivist approach of teaching spelling and pronunciation from a relatively small number of texts, with Webster's dictionary being a major contributor.
Simultaneously, students from many backgrounds, many knowing no English at all (their parents having recently emigrated from Norway or Italy or Germany, for example), were thrown into these schools. Parents, teachers, and the general public saw this as an opportunity to teach children the "right" way to speak English, and so the teachers were even more motivated to rely on Webster's dictionary to achieve a "universal" result.
Certainly this progress was "chaotic" (universal primary education took a full century to spread across the whole country, for example), but the progress was steady and strongly motivated. (The "motivation" occurred at all levels — local, state, and federal. While no one loved taxes even back then, most people saw the merits of public education and were, for the most part, willing to contribute their fair share.)
But the result of this is that Americans, in spite of their diverse backgrounds and the wide distances between many population centers, speak/spell a relatively standardized language. This is especially the case when one gets away from the East Coast (whose populations predate the universal education movement).