This is a great question. Because my expertise is in nineteenth-century British science and culture, my answer to your question will favor the Victorians. However, most of the technological transformations that Victorians encountered were transatlantic developments, so they were also happening in America.

Believe it or not, Great Britain in 1900 would have been fairly recognizable to us: it had trains, electric lighting, a global telegraphy network, and even early radio (then called "wireless telegraphy"). If you move your timeline up a bit, you are absolutely correct in saying that the century's changes "must have been a huge culture shock" for Victorians. For those born in the 1820s, the first railway lines cut through rural towns, estates, and landscapes that had been (for the most part) unchanged for a long time. When the first lines opened in the 1830s, opponents of the railway included the poor and the landed gentry alike. George Eliot's novel, Middlemarch, details how a small rural town might have responded to railway construction. For a good non-fiction resource, Laura Otis's book, Networking: Communicating with Bodies and Machines in the Nineteenth Century, argues that the image of the "world-wide web" begins with the webs and networks created by Victorian technologies and metaphors, including the telegraph, the multiplot novel, and the railway. When she discusses the railway, she explains that the landed gentry felt threatened by these trains whose lines now cut across their estates. The poor, also, remained convinced that a new technological development would worsen the quality of their lives. What the railway did do was alter Victorians' perspective of space and time. They could now travel very quickly. The railway also centralized the book market, which made print materials both more accessible and more ephemeral. Print materials were not only shipped and circulated by train, but they were commodities for the train. Novels were sold at stations, just as we now see magazines and books at airports.

Technologies, though, do not exist in isolation, so when the telegraph emerged in the late 1830s - early 1840s, it did so as a companion technology to the railway. Telegraph lines were constructed alongside railway lines, which was a measure for preventing railway accidents. Until this point, time was not standardized. Each station had a slightly different time, and time zones had not been established. The telegraph's introduction to the railway system necessitated time standards across stations. For more on this, Andrew Herod's book, Geographies of Globalization: A Critical Introduction is a good resource.

By the mid-nineteenth century, Britain was celebrating its technological prowess. In 1851 in Hyde Park, Queen Victoria opened The Great Exhibition (or, as Punch magazine dubbed it, "The Crystal Palace"). This was an enormous celebration of industry and progress, attended by very famous members of society, as well as common people.

Britain's first successful transatlantic submarine telegraph cable was completed in 1866. This was a game changer. The British could now communicate with America in a matter of minutes. After 1866, Britain expanded their global telecommunications network and their empire, with lines connecting to North America, the coasts of Africa and South America, India, Australia, and Asia. For more on the telegraph and globalization, I suggest consulting Roland Wenzlhuemer's book, Connecting the Nineteenth-Century World: The Telegraph and Globalization. Any of Bruce Hunt's books on telegraphy would also be excellent, although Hunt concentrates on the history of science which allowed the telegraph to be globally successful.

Victorians also encountered both electric lighting and wireless telegraphy before the turn of the century. Chris Otter has a book that I'd recommend on the cultural and political reception lighting, including electric: The Victorian Eye: A Political History of Light and Vision in Britain, 1800-1910. On wireless, I would say that Guglielmo Marconi patented this technology in 1895, but the science behind what we'd now call early radio was still largely a mystery. Wireless telegraphy found immediate usefulness as a ship-to-shore technology, since cable telegraphy could not be used to communicate with those at sea. Since Britain was the leading naval power at the end of the nineteenth century, wireless telegraphy was a valuable tool.

Hopefully this answers your question! Although the end of the nineteenth century was an important period of change, for example, Einstein's theory of relativity in 1905 shifted physics entirely, the entire nineteenth century, even the beginning, was an enormous period of transformation and cultural change. There were plenty of scientific shifts during the nineteenth century, too. I haven't covered those because I felt that they were somewhat outside the scope of your question, which centered on technology and culture.

Well that depends on a lot of things. To answer your question I'll be examining Time, Place, and the very changes themselves on a personal and societal level.

So first we'll look at time. Depending on what you mean by the Late 1800's, the era of change had already been occurring for a good while. Industrialization has its roots in the late 1700's in England, and increased in both scope and scale from there on out. Someone born in the 1850's (depending on where they are from, which I'll get to in a minute) would already be familiar with the idea of factories and the advance of scientific pursuits by the time they reached adulthood. Electricity, which had been known as a novelty since at least the 1700's, had already been used to transport information via the Telegraph by 1837, and electric motors soon after that. Someone born in the 1890's would be younger than the automobile (which was either invented in the 1870's or 1880's depending on what you count as a "car"). So while someone born in the late 1800's would certainly be living through times of great change, they and those around them would have been aware of this accelerating trajectory for decades.

Next we'll look at space. As with the modern day, where you live greatly affects your access to technology. I mentioned this before, but the industrial revolution and this era of rapid change has its roots in England and spread outward from there. The early adopters were those closest to England in the Economic and Political sense, with the United States and North Western Europe dominating the scene. The previous section about time talks about how someone living in these areas might experience this change, but in this section I will focus on the nations who didn't have that early advantage. As the balance of the world's economics and politics increasingly concentrated on Western Europe (and to a lesser extent the United States), nations outside of that frame had a myriad of reactions, and I'd like to focus on two of those nations: Japan and China.

Chronologically, China realized the pains of behind the curve earlier than Japan did, with the Opium Wars in the first half of the 1800's putting China thoroughly in the sphere of the British. Following that, the Century of Humiliations saw China increasingly cede its place in determining its own affairs to Western Powers. While individuals within the government advocated for modernization, the institutions as a whole had such an inertia (as would any 2000 year old society) that they proved incapable to adaptation. The Century of Humiliations was one of the greatest eras of unrest in China, with the Taiping Rebellion, the First and Second Opium Wars, the Boxer Rebellion, the First Sino-Japanese War, and the eventual ending of the Imperial Government of China with the creation of the Republic of China which itself fell to regional warlords by the 1920s.

So while China represents what happened to governments who didn't/couldn't adapt, Japan represents those which could. The Meiji Restoration of 1868 was not as smooth a transition as it is often portrayed. The Imperial government felt much resistance from both the people and factions of the old government. The Boshin War was one such example, where Samurai loyal to the Shogunate resisted the ascension of the Emperor to political primacy. Moreover, there were numerous riots in Japan with each step of replicating modern (read Western) society, including resistance to Public Education, Universal Conscription, ending the privileges of the Samurai, and reforming the government and constitution. Dan Carlin has an excellent Podcast covering this transition in Supernova in the East.

Finally, I'd like to cover the changes themselves, or rather the trajectory of change. How people respond to change, at least in the long term, largely depends on how that change has worked out for them. So as I showed with China and Japan, when the changing world leaves you behind, and the people left worse off (in reality or in spirit) than they were before, the people and government grow restless. Some resist the change until their populace boils over like in China and the Russian Empire. Others desperately play catch up, with varying degrees of success. Japan is the poster child of success in this effort, but people often forget about the arguably less successful efforts made in the Ottoman Empire, Persia, and even Ethiopia. The most striking example might be Germany in the aftermath of the First World War. The rapidly changing world had them on a steep upward trajectory in the world, and they felt cheated out of their place in the sun in the post world environment. Change had left them worse off, and thus they turned to new ideologies to rectify that.

People from all over the world reacted very differently depending on how that change affected them. Some, for whom felt change would be for the better, reacted by embracing the change. Many people were attracted to various Socialist, Unionist, and Technocratic movements, and made active efforts towards ushering in a new age of science, innovation, and plenty. Others, who felt that change would leave them behind or was somehow unnecessary, resisted that change, and turned towards cultural and religious movements that harkened back to the good old days.

You were very right to draw parallels to the modern day with the Internet. In fact, I would say that the interaction of modern computing and the Internet is far more revolutionary than the slow transition from the candle to the lightbulb. If you want to see how people back then might have reacted to change, take a look at the elderly and computers. Some embraced it seamlessly. Some like it, but struggle. Some hate it. Technology changes, and will always change. People, however, are just more of the same :)