Salamanders are, of course, real creatures - long-tailed amphibians with a vaguely lizard-like appearance. The Ancient Greeks and Romans attributed a number of magical abilities to them, some of them related to fire, but it's clear that they were describing the real animal when they did so. In the Middle Ages, however, there's more of a split between the amphibian and the fantastic creature, with the latter taking on more exotic forms and powers. This culminates in the 16th century with Paracelsus adopting the name for what he termed "fire elementals" and it's this that's most likely the inspiration for the D&D monster.
1E
The salamander in 1E is roughly humanoid from the waist up, with the legs replaced by a single tail that keeps the creature in broadly human proportions. A series of narrow frills extends along the back, and also down each of the arms; these are partially erect, but whether they are buoyed aloft by hot air or are self-animated tendrils isn't something we can determine from the picture. The head has a flattened cranium and a triangular jaw with sharp carnivorous teeth. The ears are significantly elongated, with further frills on them and a pair of branching tendrils project out from either side of the nose, which we might suppose to be sensory. The creature has a partly striped and partly mottled pattern, with the background colouration shading from yellow to red along the length of the body.