Hi there,
Certainly the most common condition to rule out first would be 'hot spots', ie focal areas of pyoderma (a bacterial skin infection) by treating with a good broad spectrum antibiotic (amoxicillin/clavulanate is usually the first choice). In addition to this I would scrub the affected areas with some Chlorhexidine (Hibiscrub) on some wet cotton wool. I would also at this stage give an injection of dexamethasone to settle down the inflammation and take away the itchiness. Finally, I would rule out parasites by applying a prescription veterinary spot-on that is effective against sarcoptic mange.
If all that was done, and the lesions are still there, then it is unlikely to be bacterial or parasitic in nature. I would then do a Woods Lamp or Fungal culture to look for Ringworm, and possibly take a bacteriology swab in case of resistant bacteria.
If those tests were negative, you would probably need to do skin biopsies. This would usually provide a definitive diagnosis, but may require a general anesthetic to take good deep biopsies. If something rare was the cause, such as autoimmune disease or cutaneous lymphoma, this would be the only way of diagnosing it.