Legal marriages are typically governed by statutes in each individual state. From the The 2010 Florida Statutes online:
Chapter 741 - Marriage; Domestic Violence
741.07: Persons authorized to solemnize matrimony.--
(1) All regularly ordained ministers of the gospel or elders in communion with some church, or other ordained clergy, and all judicial officers, including retired judicial officers, clerks of the circuit courts, and notaries public of this state may solemnize the rights of matrimonial contract, under the regulations prescribed by law. Nothing in this section shall make invalid a marriage which was solemnized by any member of the clergy, or as otherwise provided by law prior to July 1, 1978.
(2) Any marriage which may be had and solemnized among the people called "Quakers," or "Friends," in the manner and form used or practiced in their societies, according to their rites and ceremonies, shall be good and valid in law; and wherever the words "minister" and "elder" are used in this chapter, they shall be held to include all of the persons connected with the Society of Friends, or Quakers, who perform or have charge of the marriage ceremony according to their rites and ceremonies.
History.--s. 1, Nov. 2, 1829; s. 2, ch. 1127, 1861; RS 2056; GS 2575; RGS 3934; CGL 5853; s. 1, ch. 28104, 1953; s. 1, ch. 74-372; s. 1, ch. 78-15; s. 34, ch. 95-401.
Notice that the Quakers felt it necessary to go to all the trouble to get their group added into the Florida Statutes.
If you are planning on just hanging out your shingle as a "Marrying Merlin" or "Marrying Merline", you might simply go the $79 Notary Public path to protect your clients from possible legal hassles. There is an online guide for Notaries "solemnizing a marriage."
You could seek ministerial credentials from fellow Pagans within a respected organization like the Covenant of the Goddess.
You can get a free online ordination from the Universal Life Church Monastery or Universal Ministries or from the Spiritual Humanist Clergy. Alternatively, you can pay for an online ordination from the Universal Brotherhood. There are more of such sites popping up online and they appeal to more than just a Christian market. Some of these groups have incorporated, hold regular worship services, attained 501(c)(3) status from the IRS, and are thus entitled to ordain clergy. Others are rugged individualists who shun any association with any form of government.
780,000+ tax exempt organizations are listed in IRS Publication 78. Although a group can be missing for whatever reason, this list can be searched by visiting http://apps.irs.gov/app/pub78
Perhaps some Unitarian Universalist congregation might be willing to name you an "elder in communion;" however, they would probably ask you to join their membership and then hang around for a while first. The UU clergy, who see themselves as "real ministers," have advanced degrees, certifications, and a rather strong union. They tend to look askance at interlopers. They might be more comfortable if you use the term "Lay Minister."
So what is an Elder in Communion? Let us say it is, "She or he who is linked by affection, association, and loyalty to a particular church and who shares in the essential elements of its spiritual values."
Be aware that in "performing a legal marriage" you are serving two roles: an officer of the State and a representative of a spiritual tradition. And people really do want meaningful rites of passage aligned with their particular values. Marriage laws vary, so be aware when you cross a state line. See more on marriage law.
Florida also makes provision for Premarital Course Providers supplying instruction of not less than four hours.
Some advice from a Florida Clerk of the Court's Office for those officiating at handfastings: