You need a foam blank, fiberglass and resin that's compatible with the blank, plus solvents, paints, cleaners...
In 1958, a shaper named Hobie Alter and a glasser named Grubby Clark perfected the polyurethane foam blank. In 1961 the two created a second company, Clark Foam, to make surfboard blanks. Soon thereafter, the surfboard was made from fiberglass, polyester resin and polyurethane foam.
There are a variety of surfboard constructions coming out now including epoxy, firewire, Solomon and many others but the traditional surfboard is a polyurethane blank and fiberglass. The polyurethane blank aka foam is shaped down to a specific shape then coated with a resin that is strengthened by fiberglass cloth.
foam
They are made of polyurethane foam. They are made of foam, but not always polyurethane foam. The king of polyurethane foam boards was Gordon "Grubby" Clark. When he closed Clark Foam, he left a big void that other technologies (like expanded polystyrene foam, epoxy foam and composite foam) helped to fill.
Mainly a Foam Compound
Surfersteve's link is listed below... I think the old-fashioned Poly- and fiberglass is your best bet. EPS foam gives me chills when shaping, plus it gets everywhere. When starting out, use UV cure Resin from that 'Surfsource' website or else maybe 'Foam E-Z' that are listed in the related links below: Get a poly- deck like a Teccel and some fiberglass with UV resin and you're in there!
acetone
The foam when broken up makes good packing materials
Fiberglass , cellulose , foam , and aluminum foil .
High density foam is just your typical foam. It does not conform to your body when it heats up like memory foam does.
Hobie Alter made some of the first foam surfboards, and he used polyurethane foam. But basically, any rigid plastic foam that won't melt when you put resin on it will work.