Plant cells, like animal or other eukaryotic cells, break down food molecules using oxygen respiration in mitochondria. The plants start with simple sugars, which are broken down via glycolysis, then bound to oxygen to produce energy. This energy process is very similar to the combustion of carbohydrates, and results in water and carbon dioxide as waste products.
Plant cells use sunlight energy directly for few processes in the cell, most notably photosynthesis. For all other functions, they use the same cellular respiration as most other organisms. Plants do generate their own energy, however, just not directly. All the calories a plant uses are derived from the sugars it makes through photosynthesis. Even carnivorous plants like the Venus flytrap use their predation to supply nutrients missing in their soils, not as a source of energy.
Photosynthesis is the opposite process of cellular respiration. In cellular respiration, glucose is broken down using oxygen, releasing water, carbon dioxide and energy. In photosynthesis, water, carbon dioxide are combined using solar energy, producing glucose and oxygen. The major difference is in the forms of energy involved. In cellular respiration, the energy produced is chemical energy, that is, energy stored in a chemical bond. In photosynthesis, the energy consumed is light energy.