Short answers, pulled from the story.
Snorri Sturluson wrote that Loki transformed into a mare to distract the stallion Svaðilfari, and their union produced a grey foal with eight legs known as Sleipnir. This event occurred during the early days of the gods' settlement when an unnamed builder was constructing a fortification for the gods.
Sleipnir appears in four specific poems within the 13th century collection known as the Poetic Edda. These texts include Grímnismál where Odin calls him the best horse, Sigrdrífumál instructing Sigurðr to cut runes on his teeth, Baldrs draumar showing Odin traveling to Hel, and Hyndluljóð stating Loki produced him with Svaðilfari.
Two image stones from the island of Gotland dating to the 8th century depict an eight-legged horse. The Tjängvide image stone shows a rider arriving at the world of the dead while the Ardre VIII image stone features a similar depiction of this steed.
Hilda Ellis Davidson argued that the eight legs represent a funeral bier carried by four bearers which could be described as riding on a steed with eight legs. The Encyclopedia of Indo-European Culture suggests the extra legs are remnants of divine twins found in Proto-Indo-European religion.
Icelandic folklore claims the horseshoe-shaped canyon Ásbyrgi was formed by Sleipnir's hoof during a ride. This legend connects the physical landscape directly to the mythological actions of Odin's eight-legged horse.