The first public announcement of photography was on January 6, 1839, in a Parisian newspaper. This referred to Louis Daguerre's invention of the daguerreotype process, developed over the past few years, though the specifics were not yet released. This news crossed the Channel quickly, particularly attracting the interest of one Henry Fox Talbot, who had independently invented a photographic process in the same period. Daguerre's process was (unsurprisingly) the daguerreotype, a positive photograph made on a silver-coated copper plate, with no negative. Talbot invented a negative-positive process on paper using silver salts: the calotype (negative) and salted paper print (positive). Talbot immediately announced his own invention to the Royal Society of Great Britain on January 31, 1839. Unlike Daguerre at this point, he explained his process in detail. However, this attracted much less public attention, due in no small part to the massive attention around the announcement of the daguerreotype process, which was promoted by the French government. The specifics of the daguerreotype process were revealed in August of 1839, expressly patent-free for the use of all mankind—except for British practioners, who had to pay to acquire the patent. Portraiture—the genre most likely to be encountered by the general public, if only the upper and upper-middle classes at this point, due to cost—was not yet practical due to long exposure times, but by the next year, 1840, further developments cut the exposure time to under a minute (with abundant light) and photographic studios sprung up. In Britain, the first photographic studio was established by Richard Beard, who acquired the exclusive patent on the daguerreotype process in England and Wales, though this did not entirely stop other photographers from practicing it commercially, most notably Antoine Claudet (who had learned it directly from Daguerre).

Talbot's paper process was not popular at this time; it was much slower and much less exact ( examples of daguerreotypes examples of salt paper prints made from calotype negatives ). However, the patent situation led some photographers to use it, most notably the Scottish team Hill and Adamson, whose work is seen in the link above. Over the next decade, French photographers made increasing use in nature photography, due in fact to its lack of clarity vs. the daguerreotype—which brings us (at last!) to your next question.

The initial art world reaction to the reveal of photography was not really to freak out. It's often repeated that the painter Delaroche reacted to the news by exclaiming "From today painting is dead!" but this is unlikely to be true. The daguerreotype was way, way more realistic than any painting—indeed, it's still the most 'high-resolution' photographic process, to a degree that can be eerie. Rather than worry painters, this reassured them. The daguerreotype was too real, too much a simple copy of nature. The dominant view among the artistic elite was that it could not be art; art was subjective while the daguerreotype was "objective." The artist was not the photographer, but nature itself. Some even went so far as to argue photography would free artists from the attempt to faithfully reproduce the world, thus furthering painting by allowing for greater expression of creative interpretation. The idea that photography was too "objective" to be Art carried on through much of the nineteenth century and into the twentieth, though it was disputed in various ways by various photographers and commentators. One of the first ways was in the fact the use of less-clear photographic processes like Talbot's paper process, or at least the interpretation of such use.

Out of the realm of high art, photography had a greater impact on commerical artists. For non-upper class folk, the most obtainable means of portraiture was the miniature, a tiny painting that was much cheaper than the kind rich folks hung in their halls. The miniature business crumbled almost immediately in the face of photographic portraiture. Daguerreotypes were not at all cheap, but they were still cheaper than those big rich folk paintings, essentially hitting the same market as miniatures. Luckily for many of the now-employed miniaturists, the practice of tinting daguerreotypes (adding colour, especially to lips, cheeks, and details of clothing) was very popular, and perfectly suited to their skills. Photographic portraiture that was affordable by a wider portion of the middle class was not around until the 1850s, when advances in negatives, papers, cameras, and the introductions of the carte-de-visite and ambrotype (one a small card-mounted paper print, the other a daguerreotype cousin made on glass) made photography cheaper, but still not cheap. Only later developments such as the tintype (popularized ca. 1860) and film and snapshot cameras (1888 +) really made photography affordable to the majority of people.

Outside of portraiture, photography only slowly advanced into illustrated books, due to the costs and complexities of its inclusion, and only really got into newspapers at the very end of the 19th century. So artists working with printmaking processes were not affected for a while, and again, only piece-by-piece.

As for the effects of photography on painterly processes, I'm afraid I can't really say with any authority; history of photography is my field, not painting. Perhaps an art historian can weigh in on that front.

I hope that has at least partially answered part of your questions!

Sources:

Anne McCauley, "Francois Arago and the Politics of the French Invention of Photography." In Multiple Views: Logan Grant Essays on Photography, University of New Mexico Press, 1991.

Lady Elizabeth Eastlake, "Photography," 1857, in Classic Essays on Photography, ed. Alan Trachtberg, 1980.

Geoffrey Batchen, Burning with Desire: The Conception of Photography. MIT Press, 1999.

Colin Ford, The Story of Popular Photography. 1989.

Frizot, Michel, ed. A New History of Photography, 1998.