Where do decomposers get their energy?

If you mean decomposition of biological material, this is mostly done by bacteria which feed off the material.They are always around and will multiply when they find a source of food. Ultra violet rays in the sun's spectrum cause decomposition of many materials, like plastics, paints, rubber etc. Oxidation especially of ferrous metal is also a main cause if exposed to rain (ie rusting). Oxygen and moisture are present in the atmosphere.