Use the hand shovel to remove some soil from the area where you need to plant the tray of grass. Measure the depth of the tray grass and remove that much soil.
Loosen the grass in the tray by flexing the sides of the tray. If you don't need the tray, you can use a scissors to cut the tray away from the grass.
Carefully take the grass from the tray and place into the shallow hole that you made. If you see any area around the new grass, fill in with the extra dirt that was dug out.
Water the grass at least twice a day for one to two weeks until it takes hold and the roots spread out. Then water once a week for at least two more weeks.