Bridges are built based on physics principles, so the engineers who design bridges have to understand physics. The opposing force of a bridge's construction has to be greater than the downward pull of gravity and side-to-side pull of wind and water. A good bridge is built to withstand every force against it--even earthquakes, in the case of San Francisco's Golden Gate Bridge. How a bridge overcomes the forces of gravity, wind, and waves depends on what type of bridge its engineer designed it to be.
Arch bridges were one of the first types of bridge. The Romans used arches in their bridges and aqueducts as well as in their triumphal arches and other great architecture. See a picture of Constantine's Arch here and Minnesota's Stone Arch Bridge here. Arches are designed with an odd number of stones, with the top, middle one being the keystone on which the bridge's weight rests. These stones have slanted sides so that they fit tight against each other. The downward force of the bridge's weight spreads out to the stones on either side of the keystone.
Truss bridges utilize the rigid 180°total angle of triangles to spread out force. A web system of sturdy beams between two girders forms a zigzagging triangle pattern, stiffening the bridge and spreading out weight so that no one section bears all the weight at that spot.
The Brooklyn Bridge in New York is one of the most famous bridges, now not so much for its size as its beauty. Built in 1883, it was the first great suspension bridge and a feat of engineering. Suspension bridges use a combination of strong cables and solid towers to achieve a balance of forces. The stone and steel that Brooklyn Bridge was built with combined to make it both solid and graceful. See a picture of it here.
For a simple project that demonstrates how one type of bridge support works, use sugar cubes to build an arch. Taper the sides of the cubes with an old nail file (or scrape them with a kitchen knife) so that they fit snugly against each other to form an arch. Be sure to use an odd number of cubes, so that there's only one cube in the middle. If you used two cubes in the middle, the frictional force between those blocks would be overcome by the load force on the arch, causing it to buckle.
If you want to learn more about bridges and construct your own models of an arch, truss, and suspension bridge, we highly recommend the Amazing Bridges kit.