How do you cure plantar warts?

Many ways. Acid therapy, freezing, burning, laser treatments, topical prescription medications like Aldara (imiquimod) and effudex, trichloracetic acid, surgical removal. See a podiatrist this is a common problem they treat.
Aspirin. Wet an Aspirin and apply nightly with tape. Another safe treatment is 5flouracil cream.
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.
Warts. Each night before going to bed soak a cotton ball in apple cider vinegar, apply it to the wart and then hold it in place with a band-aid. Leave it on all night, or if you like, 24 hours a day but change the soaked cotton and band-aid each evening for a week. The wart will swell and may throb as it reacts with the vinegar and then start to turn black within the first two days and in two weeks gone.