This is a very confusing subject. My boyfriend told me that he had genital warts 4 years ago...but that they were cured and that he is now 100% clear of HPV. We have had unprotected sex and I have not seen any symptoms on myself. He said that I had nothing to worry about.
This article in the Washington Post also says that HPV is not a big deal and that it will "run it's course":
http://www.washingtonpost.com/wp-dyn/content/article/2009/12/23/AR2009122303149.html
Not sure what to believe myself!
there's no cure but you can help your body/immune system suppress/"clear" the virus by eating healthy (dark leafy greens/fuits/veggies), no smoking/drinking(reduce drinking), no sex w/ someone who smokes (the toxins in cigaretts accelerates the virus), no tampons, exercise, take multi w/ folic acid (@ least 800mg per day), reduce stress..the procedures you mentioned don't get rid of the virus..only the possible symptoms..strengthening your immune system wil help to suppress the virus into dormancy.
HPV doesnt need treatment by cone or LEEP... those treatments are for high grade cell changes of the cervix, often caused by long lasting high risk HPV infections.
Taking good care of yourself and keeping your immune system high and limiting exposure to new types of HPV will increase your chances of it clearing on its own... which takes 6 months - 2 years.
If it's a warts variety, they can perscribe creams or do cryosurgeries I believe to remove the warts, but they may come back as the virus isn't completely gone.