Gluing fabric to Styrofoam materials requires an adhesive that will not dissolve the Styrofoam or damage the fabric. The glue should also be strong enough to ensure that the fabric will not detach itself from the Styrofoam, especially if used in a moist environment.
Many products are available to glue fabric to Styrofoam. Use low-temperature hot melt glue sticks, Tacky Glue, 3M's 77, 3M's Spray Styrofoam Glue or Aileen's Foam glue for this purpose. These products are available in craft and department stores.
Video of the Day
Never use a glue that contains a solvent with Styrofoam as this type of glue dissolves the Styrofoam. This will damage the Styrofoam, and it will release toxic fumes. When you use a hot glue, apply the glue to the fabric first. This gives the glue a few seconds to cool and causes less damage to the Styrofoam material. Use hot melt glue sparingly as it can make the fabric lumpy when it cools in clumps. Excess amounts also stay hot longer, which could cause greater damage to the Styrofoam--an important consideration in areas which can readily be seen.
Styrofoam isn't strong so don't rely on the finished product to hold much weight. A large piece of fabric hanging down could supply enough force to break the Styrofoam, even if the glue bond itself remains intact. For safety, the load placed on a bond between Styrofoam and anything glued to it should be less than five pounds per square inch of glue area due to the very low tensile strength of this material.
Working with Kids
Ensure that there is adult supervision before allowing children to use hot melt glue as the temperatures involved are high enough to cause severe burns when the glue or gun tip contact skin.