Plant Respiration:
Respiration in plants, as in all living organisms, is essential to provide metabolic energy and carbon skeletons for growth and maintenance.
As such, respiration is an essential component of a plant’s carbon budget. Depending on species and environmental conditions, it consumes 25-75% of all the carbohydrates produced in photosynthesis – even more at extremely slow growth rates.
Respiration in plants can also proceed in a manner that produces neither metabolic energy nor carbon skeletons, but heat.
This type of respiration involves the cyanide-resistant, alternative oxidase; it is unique to plants, and resides in the mitochondria.
The activity of this alternative pathway can be measured based on a difference in fractionation of oxygen isotopes between the cytochrome and the alternative oxidase.
Heat production is important in some flowers to attract pollinators; however, the alternative oxidase also plays a major role in leaves and roots of most plants.
A common thread throughout this volume is to link respiration, including alternative oxidase activity, to plant functioning in different environments.

What happens during plant respiration?
Respiration in plants, as in all living organisms, is essential to provide metabolic energy and carbon skeletons for growth and maintenance. As such, respiration is an essential component of a plant’s carbon budget. Depending on species and environmental conditions, it consumes 25-75% of all the carbohydrates produced in photosynthesis – even more at extremely slow growth rates. Respiration in plants can also proceed in a manner that produces neither metabolic energy nor carbon skeletons, but heat. This type of respiration involves the cyanide-resistant, alternative oxidase; it is unique to plants, and resides in the mitochondria. The activity of this alternative pathway can be measured based on a difference in fractionation of oxygen isotopes between the cytochrome and the alternative oxidase. Heat production is important in some flowers to attract pollinators; however, the alternative oxidase also plays a major role in leaves and roots of most plants. A common thread throughout this volume is to link respiration, including alternative oxidase activity, to plant functioning in different environments.

better explanation of the above answer stated (:
During respiration (in plants and animals) energy is released from sugar (glucose) by a series of chemical reactions. The sugar is broken down into carbon dioxide and water in a process which uses oxygen, not into oxygen.
Respiration is the chemical opposite of photosynthesis because it releases energy, using up food and oxygen and producing carbon dioxide. Photosynthesis requires energy (light) and produces food, using up carbon dioxide and producing oxygen.
Unfortunately, breathing and respiration often get confused. Respiration is the release of energy from food. Breathing is the process of obtaining oxygen and removing carbon dioxide, usually using lungs or gills. So in one sense plants don't breathe at all, although they do respire!

1. How plants breathe when they have no lungs or gills? how they respire?

~end~