If you burn yourself, you should immediately run your burn under cold water for several minutes. If you have help on the way, continue running cold water on the burn until they get there to pick you up. This will stop your skin from burning beyond the damage you have already incurred.
While finger burns tend to not be that serious, if you've burnt your face, hands, feet or genitalia you need emergency assistance and should call 911 right away.
Check for charring, if you have any charring it means that your burn has gone beyond the first layer of skin and has affected all three layers of skin. You should seek medical attention immediately if charring has occurred.
If your skin is slightly reddened but there is no blister you most likely have a mild burn. You can apply some Aloe Vera gel or other topical burn ointment to help reduce the pain.
Take Ibuprofen as needed to help the reduction of swelling and to aid in pain relief. If the pain persists, see a doctor to get prescribed a stronger pain killer.