Squeeze some antiseptic ointment onto the wound, then apply a bandage to cover it completely. In many cases a regular adhesive bandage (Band-Aid) will be plenty, but you may need to use gauze bandages and cloth tape to cover a larger scrape.
In most cases the process of treatment will be distracting enough to calm the child, but if they are still experiencing pain, you can give them the instant cold compress to hold on the wound.
If you have not been able to remove all debris from the injury with the supplies from the kit, remove the bandage once you get home and clean it again with soap and water before rebandaging.