For non-commercial boaters using vessels which are not required to have ship’s radio stations, no FCC license is required for local cruising. “Local” means USA waters only. If you cruise and sail into foreign waters of Canada, Mexico, and the Caribbean, you must have an FCC issued license and callsign. Also, mariners who operate a marine SSB and/or INMARSAT phone must have an FCC issued callsign. The FCC callsign is also required for a marine “Sailmail” e-mail address.
If you have marine single sideband (SSB) radio onboard, or plan to have one installed soon, the law requires an FCC ship station license. If you cruise to foreign ports, any radio onboard must be licensed.
Even so, you may obtain an FCC license and callsign if you want one.
Since 1999, DSC (Digital Selective Calling) capability has been required for all VHF marine radios sold in the United States. If your radio has this feature, you must obtain a nine-digit maritime mobile service identity (MMSI) and install it into the unit before you transmit. The MMSI is unique, like a phone number, and can assist the Coast Guard in finding your vessel in an emergency, among other uses. If you’re not required to have a license, the MMSI is obtained from private companies.
To obtain a license, if you need or want one, contact the FCC at www.fcc.gov. The information in this answer is located here.