To distinguish a minor burn from a serious burn, the first step is to determine the degree and the extent of damage to body tissues.

First-degree burns affect only the outer skin layer. The skin area appears dry, red, and mildly swollen. First-degree burns are painful and sensitive to touch. They should feel better in 1 to 2 days.
Second-degree burns affect the skin's outer and lower layers. The skin is painful, swollen, red, and has blisters. The skin also has a weepy, watery surface.
Third-degree burns affect the outer and deeper skin layers and organs below the skin. The skin appears black-and-white and charred. It swells & tissue under the skin is often exposed.

Treatment

The first thing that needs to be done is to cool down the burn. Use ice or cold water on the wound in order to change the temperature fast. Not doing this quickly will cause the burn to get worse and possibly spread.

Step1
Dry the wound as quickly as possible with a dry cloth or towel. Removing liquids will help prevent the spread of infection. It will also help prevent blistering.

Step2
Disinfect the area soon after drying the burn. Use something like Neosporin or another similar product to get this done.

Step3
After disinfection, apply a bandage or wrap over the burn. This will cover the burn surface and keep any objects or nasty things from getting into the skin, hopefully, avoiding infection.

Step4
In case of deep & extensive burns always take the help of qualified medical practitioner. Death in case of burns occurs due to infection & fluid loss. If not earlier due to suffocation.

Cooling helps in pain relief & you can use any otc analgesic to relieve pain. In case of burns on visisble areas get in touch with plastic surgeon so as to reduce scarring.