Why does everyone imagine Satan as red, horned, and evil-looking?

The Bible does not give Satan a set description.  He appeared in the form of a serpent to Adam and Eve (Gen. 3:1ff; Rev. 12:9; cf. 2 Cor. 11:3), and he is metaphorically described as an angel of light (2 Cor. 11:14).  Thus, the image of him being a being red in color, horned, hoofed, and carrying a pitchfork  (as well as any other popular descriptions of him throughout history) originates with man.

In reality, the attributes which make up this currently popular description of the devil are a bizarre combination of images, the majority of which are inherited from various tenets of different classical mythologies.

For example, the description of Satan having horns, a beard, and goat legs comes from the influence of the satyrs of Greek mythology.  Satyrs were fertility spirits with goat-like features (horns, beards, hooves) who were generally associated with lust, barbarity, and wickedness.  Some Bible scholars have linked satyrs with the hairy wild beasts mentioned by Isaiah (Is. 13:21; 34:14) which might have been the object of pagan worship during his day.

The notion that Satan carries a pitchfork comes from the Greek myth of Pluto, the god of the underworld.  At times Pluto was depicted as carrying a two-pronged pitchfork, mirroring his brothers Neptune and Jupiter.  Satan ended up getting the same tool in the minds of men because he was put in the same role as Pluto (being associated with the underworld and wickedness.)

The color red was not always associated with Satan.  In medieval imagery at times he was green.  Historically, the most common color associated with him is black, most likely because the Bible associates Satan with darkness and God with light.  The color red is associated with blood, violence, passion, wickedness, and the fires of hell; thus it’s understandable why Satan is commonly thought of as red.  Plus, Satan is depicted as a red dragon in Revelation 12:3.