First of all, matching means the same and coordinating means complimenting, this is important terminology to understand!
A SOLID SHIRT
Show off your necktie by putting it on a white dress shirt and remember, any color tie works with a white shirt.
Pastel coloured shirts require coordination! Pale blue shirt works with yellow, red, burgundy, gold or navy ties. A pale pink shirt works with a navy blue or burgundy tie. For a pale tan shirt, use a brown (or any shade of brown) tie. A French blue shirt goes best with a yellow, bright red, deep burgundy or gold tie.
For STRIPED SHIRTS
Determine what color is primary. Look at it from a distance. Based on that color, you can now consider the coordination required. A solid color tie would be best but a paisley pattern works with stripes. Plaid does not.
If you want to be dangerous, you could use a diagonal stripped tie. However you must ensure that the stripes of the tie and the shirt are of different sizes. Recommended size of stripes is 2:1. Make sure the stripes are twice as large as the stripes on the shirt.
A CHECKERED SHIRT (PLAID)
Do not wear a tie if you must, choose a solid tie color. Some people will suggest that a boxed pattern or dots works. If you want to try that, again, ensure you find the primary color of the shirt, and coordinate that color with the tie color.
TIE TO SUIT COORDINATION
You need to consider first coordinating a color that goes with the suit, and then once you have decided on the color, look at the pattern and follow the rules for stripped shirts.
If the suit is one solid color, the job is easy. Put any solid color tie, or any color that coordinates well with any pattern that you like.
If the suit has pin stripes (those faint thin vertical lines) then you can simply just follow the same rules as if the suit were a solid color.
Here is some advice from About.com on dressing for success!