Are there any very fast ways to get rid of some plantar warts?

A couple . The fastest ways are to freeze them off or cut them out. Acid treatments are an option but slower.
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.