Richard Goodson was born on November 16, 1941, in Enterprise, Alabama. He enlisted in the U.S. Navy on August 16, 1961, and completed basic training at NTC San Diego, California, in October 1961. His first assignment was to NAS Whidbey Island, Washington, from November 1961 to May 1962, followed by Basic Electricity and Electronics School at NTC San Diego from June to August 1962. He attended Operational Maintenance on Submarine Launched Torpedo training at U.S. Naval Submarine Base, New London, Connecticut, in August 1962, and then served aboard the submarine tender USS Bushnell (AS-15) from December 1962 to June 1963. Petty Officer Goodson next attended Underwater Demolition Team Replacement training with Class 030 at NAB Little Creek, Virginia, from July 1963 to January 1964, followed by service with Underwater Demolition Team TWENTY-TWO (UDT-22) at NAB Little Creek from January 1964 to July 1970. During this time he attended Gunner's Mate Technician A School at NTC Great Lakes, Illinois, and at Sandia Base, New Mexico, from August to December 1966, and Explosive Ordnance Disposal School at Indian Head, Maryland, from November 1968 to June 1969. Petty Officer Goodson attended Instructor training at Norfolk, Virginia, in July and August 1970, and then served as an Instructor at NAB Coronado, California, from September 1970 to April 1973. His final assignment was with UDT-12 at NAB Coronado from April 1973 until he was killed while conducting Swimmer Delivery Vehicle training in San Diego Bay on October 30, 1973. Petty Officer Goodson's remains were cremated and his ashes were scattered at sea.

His Navy and Marine Corps Medal Citation reads:

For heroism while serving in Underwater Demolition Team TWELVE on 30 October 1973. While conducting a Swimmer Delivery Vehicle operation in San Diego Bay, Petty Officer Goodson with complete disregard for his own safety and fully aware of the personal danger involved, unhesitatingly left the safety of his driver's position in a Swimmer Delivery Vehicle to push his navigator away from the turning screws of the surface craft their vehicle had become trapped under. His courageous and prompt actions in the face of great personal risk undoubtedly saved his navigator's life and contributed to Petty Officer Goodson's inability to prevent himself from being drawn into the screws. Petty Officer Goodson's selfless act of heroism was in keeping with the highest traditions of the United States Naval Service.