What are some common home remedies to treat cold sores?

Few. Most over the counter remedies are simply palliative. The acute phase lasts 10-14 days. Prescription meds such as Famvir (famciclovir) or Acyclovir given topically and orally can decrease the length of time of the acute flair up.
No good home remedy. Over-the-counter abreva plus Hydrocortisone 1% cream may help. Some other o-t-c lip balms (may have menthol) help a little with the symptoms. Cold sores on the lips or near the lips, are usually caused by herpes virus. They start as a raised reddish area, then form a cluster of tiny blisters, which break open soon, leaving a sore (ulcer) to heal up over a week. Younger babies should see a doctor.