Step 1: Identify the animal group.
Sponges belong to phylum Porifera, which have only a cellular level of organisation and lack true tissues, organs, or organ systems.
Step 2: Note the consequence of having no organs.
Because there are no specialised respiratory organs, every cell must deal with the surrounding water on its own for exchange of gases.
Step 3: Recall the water canal system.
Water enters through pores (ostia), flows through the spongocoel, and leaves through the osculum, keeping cells bathed in fresh oxygen-rich water.
Step 4: Apply the idea of diffusion.
Oxygen is higher in the incoming water and carbon dioxide is higher inside cells, so gases simply move down their concentration gradients across the cell surfaces.
Step 5: Rule out the specialised structures.
Gills belong to fish and molluscs, a moist cuticle is used by earthworms, and tracheal tubes belong to insects. None of these exist in sponges.
Step 6: Conclude.
Sponges therefore exchange $\text{O}_2$ and $\text{CO}_2$ by simple diffusion over their entire body surfaces.
\[ \boxed{\text{simple diffusion over their entire body surfaces}} \]