LEGO's building system is modular and surprisingly strong, so you can easily build yourself a LEGO bridge. Whether the bridge is decorative, a functional part of your LEGO city or even a science experiment, you can make exactly the type of bridge you need out of a few simple LEGO pieces and a basic understanding of bridges.
Measure the gap, using a ruler, you intend to build a bridge over. Most bridges cover a distance between two points, with the space between called the "gap." Measure the height and the depth of the space, and draw a diagram of it on the grid paper. Make sure you use a scale, such as one brick on the paper representing a two-stud-wide square. A stud is the knob on top of the brick.
Brainstorm and diagram your bridge using the gap. Start in pencil. Look at some of the various styles of bridges or ideas for LEGO bridges made by other people on the Internet using the guides under Resources. Your bridge needs a horizontal bridge surface and will likely need some kind of upright support system to hold it up. The support system should connect to certain points on the ground, where "feet" will hold it up.
Build the base of the vertical support. Make a solid "foot" for the bridge to stand on that's at least two studs larger on either side than the vertical struts will be. Also make it about as wide as the horizontal bridge-top will be; the base should be at least one sixth of the bridge's final height. This gives you a solid foundation for the bridge. Build one of these for each vertical leg.
Build the vertical legs up to the vertical span of the bridge. Make sure that your final design is level. When attaching bricks, make sure that any gaps on the lower level are covered by bricks on the upper levels to make a sturdier design.
Use large plates to bridge the gaps between the legs of the bridge. A plate is a wide and flat style of LEGO brick. Build up the walls of the bridge surface. If you're making a suspension bridge, you should also continue the vertical struts so that you can attach the suspension cables to the bridge. Leave the model overnight so that the pieces settle.
Test the strength of the bridge by running a model vehicle over it. The heavier the model that the bridge can withstand, the better your bridge.