Anyone can become an ordained minister with the legalities to marry people. You can even officiate at funerals, baptisms and create your own church. Under the First Amendment of the constitution it is written, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..."
Some religions have rules as to who can be ordained (to marry) within their faith. While other spiritual affiliations have no rules in this area. In every state of the United States an ordained minister can perform a wedding ceremony. However, states have their own individual laws about whether an ordained (or licensed) minister must be registered in that particular state. Louisiana is such a state that requires registration (see resources).
Ordination or licensing to become a lawful minister can be a simple process. Where some religious organisation may require years of study and, in some cases, an official educational degree, the process can also be as easy as completing the proper paperwork at an official online site (see resources). The site will send you confirmation of your ordination and present you with a certificate (license) which, in most cases, you will download and print yourself. Many of the sites that offer ordination also offer classes, church services and other information such as how to perform a wedding. If you are still unclear regarding the legalities of registration, in your area, contact your local county clerk for answers.