I have come across multiple home remedies for burn care but the one I see most often is ice. Do not put ice on a burn!
First aid for small minor burns involves running cool water over the affected area or using a cool damp compress if running water is not available. Ice (and other substances such as butter, mustard or ointments) may lead to further tissue damage.

Here is another great article from Kids Health that outlines burn care and also describes when you need to seek medical care:

Burn Care