Install and open Mudbox. Create a new project, and open the Pre-made Meshes window. This window provides a range of meshes you can modify to create different and more complex objects. The closer your initial template is to your final product, the easier it will be to create your final product.
Browse through the pre-made meshes, and find one that is closest to a dragon shape. Most users will settle on the reptile or the Tyrannosaurus Rex mesh since, like a dragon, they are both reptilian in shape and have sharp teeth. Select the Tyrannosaurus Rex or reptile mesh.
Use the UVs on the mesh to modify the Tyrannosaurus Rex or reptile to look more like a dragon. UV maps are grids -- often invisible when being modified -- with points at which users can stretch, bend and distort the image.
Modify the head of your creature to give it more of an exotic, unfamiliar look. Select the smooth brush tool, and increase its power by hitting M on your keyboard -- which increases the power of the brush. Move the brush tool over a section of the creature's head and click. You will see a dent appear in the head. Play with this tool, as well as the sculpt brush and grab brush, to create a new shape that maintains the reptilian qualities of the original mesh. Do this to various parts of the creature's body, always focusing on the final dragon product.
Using the grab tool, stretch out the neck a bit. Select the sculpt tool and create bumps all the way down the neck, back and tail. Select the grab tool and use it to pull the bumps outward, creating pointy spines. Use these tools to create more bumps and indentations on the body, to make your dragon more detailed.
Add wings by modifying the area just behind the reptile's or T-Rex's shoulders, using the aforementioned tools. Open the texture painting tool, and select a bumpy texture that best represents a dragon's skin. Select a green color, and apply the texture to the whole model using your brush.