The first thing you should do right away after your child returns with a skinned knee is to clean it off the dirt. Accumulation of dirt on the exposed skin can cause irritation and infection. Wash the wound are with normal tap water and use clean hands to rub off any physical contaminants like soil and small gravel particles. For small pieces of particles, you can use tweezers to take them out. Wash the area with antiseptic soap to get rid of any bacteria on the wound. Use warm water to wash and use your fingers gently.
Dry the area using a clean towel. Pat it dry. Now apply an antibiotic ointment to the skinned knee. It might burn a little but do not stop. Spread and massage it in with gentle fingers. You can also use an antiseptic disinfectant like dettol. Use it with a cotton ball. Hydrogen peroxide can also be used for the purpose.
Cover the knee with a bandage to help in healing and to keep dirt particles outside which can infect it. Since the skin is raw and exposed, you cannot risk anything like that. Whatever bandage you use, apply it loosely. This will allow the skin to breath and heal. Clean the wound area daily and change the bandage to keep off infection. When you change the bandage, do not forget applying the ointment before replacing the bandage. Keep using bandage till a scab layer has formed over the wound. After the scab is formed, do not irritate or pick at the wound much that there is an urge to. It is going to irritate it and disturb the healing process.