They breathe in oxygen and produce energy in the form of ATP just the same way as we do. Only difference is that 'bugs' do not have lungs, they are small enough and have a large enough surface area to volume ratio that they can get all the oxygen they need by diffusion. Some bugs have adaptations such as spiracles that allow them to 'absorb' more oxygen more efficiently.
Furthermore, plants too utilize oxygen in exactly the same way as animals and bugs!
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