Short answers, pulled from the story.
Tolkien stated that he wisely started with a map and made the story fit, attending with meticulous care to distances. He found that composing a map from a finished story leads to confusions and impossibilities, so the map came first and the plot was built around it.
The Lord of the Rings contains three maps and over 600 place-names. The maps include a large drawing of the north-west of Middle-earth, a detailed map of part of the Shire, and a contour map of Rohan, Gondor, and Mordor drawn by Christopher Tolkien.
Pauline Baynes painted the iconic poster map of Middle-earth. Allen & Unwin commissioned it in 1969, Tolkien supplied her with copies of his draft maps and annotations, and the publisher released it as a poster in 1970.
The frontispiece map in William Morris's 1897 novel The Sundering Flood is considered the first fantasy map in the modern sense. It depicted a wholly invented world with a great river, a Desert Waste, and towns with English names like Westcheaping and Eastcheaping.
Geologists have identified several problems, including right-angle junctions in mountain ranges around Mordor and the Misty Mountains, which do not match how plate tectonics form mountains. The river Anduin runs parallel to a mountain range rather than away from it, and one of its tributaries forms a delta where no sea exists.
Christopher Tolkien drew the contour map of Rohan, Gondor, and Mordor from his father's detailed pencil, ink, and coloured-pencil design. He worked for twenty-four hours straight, from six in the morning to six the following morning, to finish the redrawing just in time for publication.