This is the most common question people ask me. The philosophy behind both forms of medicine are relatively similar. They both aim to find the root cause of disease and remove it and stimulate the body to heal itself. There is one difference: Homeopaths only use homeopathy and maybe some lifestyle counselling. Naturopaths use many different types of medicine, such as acupuncture, Chinese medicine, herbal therapies, vitamin therapies, lifestyle counselling and homeopathy.
Naturopaths' large toolbox gives them a unique ability to determine what therapy is best for you and if one therapy doesn't work, they have lots of others to try. However the breadth of their knowledge does not always translate into a depth of knowledge. The homeopathic schools I know in Ontario teach 10 times the amount of information on homeopathy than a Naturopathic college does, with hundreds of hours of clinical, homeopathic, experience included in the degree. Therefore if you know you would like to try homeopathy, I suggest finding a licensed homeopath. Regulations are always changing and different in every country/state/province, so I can't recommend a universally good place to look for a homeopath. If you are in Ontario, as I am, then you want to see a homeopath that is licensed by the Ontario College of Homeopathic Medicine.