The archetypal Red Dragon is Smaug from "The Hobbit".
Dragons grow more powerful as they age. Generally, a newly-hatched Red Dragon should be given 1 hit point per die, while a very ancient one (in excess of 400 years old) will have 8. All dragons share certain special characteristics: they can sometimes speak, sometimes use magic, will sometimes be found asleep, possess powerful magical breath weapons, can cause fear in weaker opponents, are tough and magic-resistant themselves, and can in some circumstances be subdued.
Red dragons usually (80%) speak, sometimes (40%) cast magic, and will sometimes (20%) be found asleep. If the dragon is asleep, there is a 1 in 6 chance that it will awaken in the presence of adventurers. Dragons also sometimes feign sleep.
If a red dragon can cast spells, it will do so as a magic-user equal to its age category. Thus a red dragon with 6 hit points per die can cast spells as if it were a 6th level magic-user. Owing to the magical nature of the creature, it does not require somatic (hand gestures) or material components to its spells - it need only speak the incantation.
Red dragon breath is a cone of flame, 90ft long and 15ft radius at the base, emanating from the mouth of the creature. It does damage equal to the dragon's hit points (but a save vs dragon breath halves this amount). The dragon may use this breath weapon up to three times per day.
Red dragons cause fear (as the spell) in creatures of less than 5th level unless they save vs magic.
If issued with a formal challenge, a dragon will sometimes agree to fight until subdued rather than to the death. The GM should rule about the likelihood of the dragon's acceptance and the conditions that apply, since these will depend on the nature of the challenge.
Red dragons with 5 or more hit points per die gain a bonus of +1 to their saving throw rolls per hp/die in excess of 4. Thus an ancient red dragon with 8hp per die saves at +4.