Plants get nutrients by absorbing them from the soil and also by forming sugars through photosynthesis. Photosynthesis is the process whereby plants absorb light energy from the sun to convert carbon dioxide and water into sugar.
Plants contain vessels, similar to arteries, that transport nutrients and water around the plant. Water is absorbed by the roots of the plant into transport vessels called xylem. Sugars are transported in vessels called phloem. Both xylem and phloem act as the vascular structures that feed nutrients to every part of the plant and help it grow.
The other method by which plants obtain food, photosynthesis, occurs on the leaves of plants. Leaves are a particular shape to maximize the surface area to absorb as much light as possible. This is also why plants grow upward, as they are in direct competition with other plants for light. The leaves absorb this light as a form of energy, which can be used to form sugars inside the plant.
Veins are present across the face of a leaf. The plant uses the veins to move water and food, helping the plant grow. The combined effect of water absorption from soil, photosynthesis and this vascular architecture is what is responsible for the production and delivery of nutrients to plants.