How can I reduce the appearance of sunken eyes?

Hydration and rest. This appearance is more common with dehydration and fatigue. The easiest treatment is to stay well hydrated (drink plenty of water and non-caffeinated beverages) and to get more sleep.
Sunken Eyes. Sunken eyes often due to fat atrophy/loss around eye (due to genetics often); see an oculoplastics eyemd to discuss options.