When pulling the tooth out, be sure to pull it straight upwards. Bleeding may occur but you can wipe that away with a cotton bud or a clean, wet cloth. Over the counter anesthetics can also make this easier such as the teething gel, Bonjela. Children (strangely) have a much higher tolerance to pain so if anything, pulling a tooth out will probably only discomfort this child or panic them into crying.
While allowing the tooth to fall out naturally, eating may become an issue. By eating hard foods, the tooth will become loose and you will hardly even notice it fall out. This is a great method for young children as they will not notice the tooth loss hence, not feel any pain.
Another method is the floss method. This involves putting a string of dental floss around the tooth and pulling it straight out. This is quicker so the pain will only be for a few seconds though getting the courage to do it may be harder.
After the tooth has been removed, the gums will be very sensitive so avoid eating on or around it by eating with the other side of the mouth, and eating softer foods. Make sure the mouth is cleaned and rinsed correctly after removing a tooth to avoid gum problems and infections. Corsodyl mouth wash is the best for gum problems and dentists often prescribe it though it is also available over the counter.