Well, the cheap and easy way:
On a cloudy day with indirect lighting, get outside and put the cue on a piece of cloth. The indirect lighting (no direct sun) will give you good light without harsh shadows and without disturbing reflections. The late afternoon is better than noon, because the light is even smoother.
Most cameras have a white-balance setting for cloudy sky, this gives a warmer impression. Otherwise, the pictures might be somewhat blue-greyish.
Second alternative: If the sun is bright, get inside and avoid direct sunlight. A room with white walls will give good light as well.
If you want to stay outside: Wait for the late afternoon, this will give a less harsh reflection. If the shadows are too strong, put a piece of polystyrene onto the shadowy side, this will reflect the sunlight and brighten the shadows.
If you use a flash, it's better to use a flash which does not shine directly onto the cue, but which reflects from the ceiling or shines from the side. If you need to use the built-in flash, you can improve the light with a piece of paper, i.e. one or two layers from a handkerchief.
Avoid neon lighting, this will result in bad colour reproduction and often in a green tint.
Regards,
Detlev