Yes — all living beings respire, and plants are no exception.
How a plant does it: there are tiny pores called stomata on the surface of the leaves. These pores let air move in and out of the plant. Roots take in the air present in the spaces between soil particles, and woody stems have tiny openings of their own.
Try This — the activity the book suggests: ask the senior students of your school to show you stomata under a microscope. Peel the thin lower skin off a fresh leaf (a Rhoeo, money plant or lily leaf works well), put it on a slide with a drop of water and look. You will see tiny mouth-shaped pores, each between two curved cells.
A common confusion cleared: a plant makes food in sunlight, and it respires all the time. These are two different processes. In bright sunlight the food-making is much faster, which is why we usually notice only that one.