Several treatments. You can try over the counter wart removers, but be careful: I've seen them do more harm than good. Other options your doctor might offer include cryotherapy (freezing the wart), electrocautery (burning the wart), laser treatment, or several different topical chemical treatments. If the treatment is typically uncomfortable, your doctor can numb the area before proceeding.
Same way. Treatment will be same, 8 or 80 year old, starting with local care, if fails, excision or fulgarization. In a child may need short general, as kid may not cooperate for local anaesthesia.
Topical medication. Topical medication can be used to treat the warts over multiple treatments. The big porblem is gaining the childs confidence to allow the doctor to trim the skin over the wart.