Answer by taking a quote from the following article:

Flotsam and Jetsam is an American thrash metal and progressive metal band that formed in Phoenix, Arizona in 1981. The band currently consists of vocalist Eric A. Knutson, guitarists Michael Gilbert and Steve Conley, bassist Michael Spencer and drummer Ken Mary. Flotsam and Jetsam went through several lineup changes over the years, and Knutson has been the only constant member of the band. They are also notable for featuring bassist Jason Newsted, who left the band shortly after the release of their debut album to join Metallica as Cliff Burton's replacement.

The group was founded in 1981 under the name Paradox by drummer Kelly David-Smith and guitarists Pete Mello and Dave Goulder, who were later joined by bassist Jason Newsted. Jason had answered a newspaper ad that Kelly had placed in the local newspaper looking for a bass player. Jason came to Phoenix with his band Gangster from Michigan on their way to California, but Gangster broke up while in Phoenix. Kelly got a call from a couple of his high school friends, Mark Vasquez and Kevin Horton, looking for some people to jam with playing covers of bands such as Iron Maiden, Judas Priest, MSG, and UFO. The band then morphed into "Dredlox" together with the new recruits, Jason was now the main vocalist.  Kelly saw "A.K." (Eric A. Knutson) singing "The Goodbye Girl" at his high school talent show. In 1982 they were in the same summer school class and Kelly asked Knutson if he wanted to audition. They put him on 2-week probation and he later joined the band. Due to the provisional nature of his membership, the band referred to Knutson as "the 2 weeker." Ed Carlson, from another local rival band called Exodus (not to be confused with the California Bay Area thrash metal band of the same name), also joined in 1983 after Kevin's departure from the band. The name of the band changed into The Dogz, but it didn't last long. Eventually the band renamed itself "Flotsam and Jetsam" after writing a song inspired by a chapter of J. R. R. Tolkien's The Two Towers.  The band made its live debuts in local clubs and in California and had the opportunity to play with bands such as Megadeth, Armored Saint, Alcatrazz, Malice, Exciter, Mercyful Fate, Riot, Autograph and Icon. In 1985 Mark Vasquez stepped out and 17-year-old Michael Gilbert joined the band. Flotsam and Jetsam released two demo tapes Iron Tears and Metal Shock in 1985.  They created their first video "Hammerhead" from the Metal Shock demo: "We taped it in Jason and Ed's apartment living room. We also made a live video at the infamous Bootlegger in Phoenix", (owned by Gloria Cavalera, currently married to Max Cavalera) These videos and the band's demos made a good impression on record labels. After the band contributed to the Speed Metal Hell II and Metal Massacre VII compilations, they then signed a deal with Metal Blade Records.

How did the bandmembers first meet each other?
Jason had answered a newspaper ad that Kelly had placed in the local newspaper looking for a bass player.