The half-dragon character work as same as the other standard races in AD&D, an half-dragon depending of the type of his draconic parent can become almost any class except for the paladin and druid that are eligible only for human, but I wrote special kits for half-dragon that give them some aspirations specific to their race.
Three species of metallic dragons have the natural ability to polymorph into human or demihuman form: gold, silver and bronze dragons. Sometimes while in these polymorphed forms, the dragons enjoy the company of the humans and demihumans. These encounters sometimes produce offspring of mixed heritage – the half-dragons. These three types are the most common (if any) half-dragons encountered in a campaign.
Half-dragons are only born from human or demihuman females. Polymorphed female dragons never produce offspring from dalliance with human or demihuman males, however a male dragon using a polymorph self spell can produce half-dragon offspring: this explain the origin of half-chromatic and half-gem dragons. Half-chromatic dragons are created by rogue chromatic dragons (i.e. those rare chromatic dragons who tend to go against their basic nature by being either neutral or good). Few physical features definitively mark a newborn babe as a half-dragon, though there are telltale signs of a dragon parent – usually hint of gold, silver, bronze, red, etc in their hairs and skin or eyes with oval pupil or of typically draconic color (ex: having a purple iris). However, some half-dragons will definitively show evident signs of their draconic heritage: wings, tail and horns above the temples. Usually half-gold tend to have blond hair, half-red tend to have red hair, half-amethyst will tend to have deep purple-blue eyes, etc… However all normal available colors and shadings for hair, eyes or skin are possible. If the colors of the hair or eyes are not those of the dragon parent, they usually give a faint reflection of the color of his or her draconic parent.
As they reach adulthood, half-dragons grow tall and lean, no matter what human or demihuman blood mixes with their draconic heritage. During late childhood and the adolescence, draconic abilities begin to manifest themselves. These abilities become stronger and more pronounced with time and use, until a half-dragon come to his or her full power. Physical changes accompany the appearance of these abilities, eventually metamorphosing a half-dragon into a captivatingly beautiful and unique being.