It was called the "Sholes & Glidden Type Writer," and it was produced by the gun makers E. Remington & Sons in Ilion, New York from 1874-1878. It was not a great success (not more than 5,000 were sold), but it founded a worldwide industry, and it brought mechanization to dreary, time-consuming office work.

The idea began at Kleinsteuber's Machine Shop in Milwaukee, Wisconsin in the year 1868. A local publisher-politician-philosopher named Christopher Latham Sholes spent hours at Kleinstuber's with fellow tinkerers, eager to participate in the Age of Invention to produce devices to improve the lot of Mankind.

It's said Sholes was working on a machine to automatically number the pages in books, when one of his colleagues suggested the idea might be extended to a device to print the entire alphabet. An article from "Scientific American" was passed around, and the gentlemen nodded in agreement that "typewriting" (the phrase coined in SA) was the wave of the future.

Sholes thought of a simple device with a piece of printer's type mounted on a little rod, mounted to strike upward to a flat plate which would hold a piece of carbon paper sandwiched with a piece of stationery. The percussive strike of the type should produce an impression on the paper.

Sholes' 1868 demonstration model looked like this:

With the key of an old telegraph instrument mounted on its base, Sholes would tap down on his model, and the little type jumped up to hit the carbon & paper against the glass plate. There was nothing for spacing, line advance or any "normal" typewriter feature. Those were all to come. It seems silly, but in 1868, the mere idea that type striking against paper to produce an image was totally new. It needed proving, and the little telegraph key model did the trick.

With the point proven, Sholes proceeded to construct a machine to do the whole alphabet. The prototype was eventually sent to Washington as the required Patent Model. The original still exists, locked up in a vault at the Smithsonian:
Sholes'original prototype and patent model. This diagram shows Sholes' basic "up-strike" design. The actual printing type is mounted on the end of a "type-bar." Pressing on the key swings the type-bar up toward the cylindrical platen, with a ribbon for the inking. The typing was, therefore, hidden from view, and so the machine was called a "blind-writer." The carriage was hinged so the user could check the work.
Investor James Densmore provided the marketing impetus which eventually brought the machine to Remington. Sholes lacked the patience required to penetrate the marketplace, and sold all of his rights to Densmore, whose belief in the machine kept the enterprise afloat. Remington agreed to produce the device beginning in 1873. The "Glidden" part of the name came from Carlos Glidden, one of the Kleinstuber Machine Shop gang, who had been something of a help to Sholes.
The original Type Writer was heavily decorated with colorful decals and gold paint. A foot treadle was provided for the carriage return. If you think it all looks a lot like an old sewing machine, you're right. No coincidence, though. William Jenne, the Remington engineer who set up the typewriter factory had been transferred from Remington's sewing machine division.

The original Sholes & Glidden used the QWERTY keyboard, but typed in capitals only. It was a sluggish, finicky, inefficient machine. In five years, only 5,000 were sold, but Remington had plans. In 1878, the No. 2 machine was introduced. It typed both upper and lower case, using a shift key. Gone were the decorated panels in favor of a black open frame (which turned out to be quieter), establishing the archetype open-black-box look typewriters would have for decades to come. It took another decade, but the "Remington No. 2" became a huge success, and the Typewriter Industry was on its way.
Sholes & Glidden Type Writer, 1874. Treadle model. A table model was also offered with a handle at the side instead of the foot pedal. Among the first users was Mark Twain, who fiddled around with it before putting it aside. Yes, Twain did become the first person to submit a novel in typed form to the publisher, but that wasn't until much later ("Life on the Mississippi,"1883) , and he didn't type it himself... it was a typed copy of his handwritten manuscript. Twain fans, by the way, might cite his autobiography, which says "Tom Sawyer" was his first book submitted in typescript. Not so. The old fella remembered it wrong, and careful research by Twain historians has proven otherwise.

Thanks to Darryl Rehr: for this superb information on typewriters. If you have further interest please contact him.