This article will show you how to use a router safely and offers some tips to stay safe and produce a quality piece of work.  When using a router, or any power tool, you should always exercise safe practices.  It is important to keep in mind that routers are powerful tools and can be dangerous.  When using a router, always stay focused on what you are doing, and respect the tool you are using. 

Safety Guidelines:
Always use a sharp router bit.  Dull router bits can not only affect the quality of the work piece but can also be very dangerous.
Dull router bits put more stress on the router and usually end up burning the wood.  Using dull router bits can also catch the wood and cause the router to twist out of your hands. 
Always make sure your work is clamped down securely.  You can get wood clamps made specifically for this.
Feed the router from left to right so that the cutting edge meets the wood first.
Use shallow passes, going deeper into the wood with each pass.  Making too deep of a pass can burn the wood, or even cause the router to twist out of your hands.
Don't ever push the router; allow the router to move through the wood more slowly.  Feeding the router too quickly can cause the wood to burn, splinter, or chip.

Tips and Tricks
Fasten a piece of wood the same thickness of the work piece to the router table or bench so that it can serve as a support for the router.  This will prevent the router from wobbling while you make the cuts.

Use an edge guide whenever possible.

Watch for knots, warps and nails in the wood you are routing.
Never use a router on wet wood.

There are different techniques you can try when using a router.  Different techniques may work better for different types of router bits being used and different types of desired cuts.

Edge Profiles:

When routing edge profiles make sure your work piece is clamped down securely by using a wood clamp.
Move the router in a counter clockwise motion around the outside of the work piece.  If your cutting the inside of a piece, cut clockwise. (you should also cut clockwise around the top right corner of the piece and the bottom left corner of the piece and then go around the entire piece counter-clockwise.  This will prevent splintering at the corners.
Make shallow passes with the Edge Bit, going deeper with each pass. You may want to test the router on a piece of scrap wood to see just how shallow you need to make each pass. Different woods may chip easier, and for certain pieces you may need to take more shallow passes than others.
*Keep in mind that if you’re cutting your piece with an edge trim bit, you need to sand your work before routing.

Dado Cuts:
Dado cuts make grooves in wood. you can make dado cuts in wood using a router with a striaght router bit and a router jig or a T-square.  Choose straight router bits that will create the desired groove width.  Test the router bit by using the router on a scrap piece of wood to ensure it will make the desired cut.  Then clamp the T-square to the work piece and make the desired cuts.
Route on the right side of the T-square or jig so that the router pushes against the securely clamped jig instead of away from it.  This will ensure straight even dado cuts.