Officiating at weddings used to be strictly the province of clergy and judges. These days, however, it's not uncommon for couples to ask a friend to perform a ceremony, for example as a notary public. Other people just like the idea of being able to marry two people in love. The exact requirements for obtaining legal authority to perform a marriage vary from state to state; in Kentucky, only religious figures and judges can do it.
Become a judge or justice in Kentucky and you have the authority to perform weddings, even after you retire. Ministers and priests "of any denomination in regular communion with any religious society" also have that power. Religious groups that do not have priests or similar figures may perform marriages communally.
Visit the county clerk in whichever part of Kentucky the wedding will be held and request a license to perform marriages.
Even if you're licensed, it's illegal in Kentucky to "solicit, persuade, entice, direct or induce" couples to come to you for the ceremony, or to have someone else do it on your behalf.