Reach into your imagination and childhood to come up with fantasy figures. Fantasy art is abnormal but is based on reality that has been molded into unreality. Take two creatures, such as a human and a horse and you come up with a creature that is half man and half horse. The image is based on two real subjects just turned into something ridiculous.
Brainstorm your ideas. Think about what sort of fantasy characters you would like to create and start doodling your ideas down on a sketchpad.
Perfect your drawing of human faces and animal's body. Many fantasy art creations start off as human and then intertwine into an animal's body. By perfecting your drawing of animals and humans, you will become comfortable to use both forms to create one mythical creature.
Use a reference to help you with creating your art. Look through fantasy magazines and books to get your imagination going. Referencing art can help get your creativity flowing and your art can stem off from an art form that has already been created, but with your own taste and ideas added to it.
Carry a sketchpad wherever you go. When you get an idea for a fantasy art creation, you will be able to sketch it down right away while the idea is still fresh in your mind.