Plants have a vascular system. This is the process by which they pump the water all the way through the plant. So an easy way to understand this is that the larger the plant, the larger the vascular system that it has.
The vascular system also moves nutrients throughout the plant.
An example of a tree that has a very large vascular system is the Sequoia. The Sequoia is a very tall tree, measuring up to nearly 380 feet tall.
Vascular systems in plants differ. Some systems use xylem and phloam which are tissues. These are found mainly in trees. The xylem is located towards the middle of the plant and is generally responsible for transporting water. The phloam is under the bark and is responsible for transporting nutrients.
Plants use vascular bundles. They contain both xylem and phloam as well and work in generally the same same way.
Water is one of the substances plants use during photosynthesis: water + carbon dioxide (+energy from the sun) --> oxygen + carbohydrates. In other words, all life on earth depends on the ability of plants to produce stored energy in the form of carbohydrates (sugars). This process takes place in the chloroplasts, mostly in the leaves. Carbon dioxide is absorbed from the air, water from the roots. And as you say in your question, sometimes the water has to travel hundreds of feet. Water travels through specialized tissue called xylem, which is essentially a series of tubes and support tissue. As water is used in the leaves, more is drawn up through capillary action, a tendency of water particles to attach to each other.
Plants need so much of water because, by weight most of the weight of all plant consists of water. Further, please remember that the total water that we may use for watering plants in a garden is not absorbed by the plants. As a matter of fact most of the water either through watering the plants, artificial irrigation, and natural rainfall is absorbed by the soil and through a long and complicated process gets converted back into clouds that give us rains.
There are some specialized methods of irrigation, such as drip irrigation, which enable growing of plants with very limited amounts of water by minimizing the loss of water through absorption of soil and evaporation in the atmosphere.
The water that is present in the soil is first absorbed by the roots of the plants through the process of osmosis. The water containing nutrients needed by the plants so absorbed is then "pumped" or "raised" to leaves through process of capillary action, which causes liquids to rise up in very thin tubes or passages, called capillaries. to rise up the capillaries because of the forces of attraction that exists between the liquid and the walls of the capillaries.