How long does it takes for an std to lead to complete infertility ?

Varies: Depends upon to which std you are referring. Even if we focus on one of the more common leading to infertility, e.g., chlamydia, this focuses on the degree of inflammation created in that person's fallopian tubes and elsewhere, and how long it goes on. Sometimes scarred and obstructed tubes can be reopened by skilled surgeons, sometimes not. There are other ways in which infertility occurs.