The easiest way of matching your color (and this goes double if you order custom vinyl siding colors) is to purchase a couple of extra panels when you buy your siding, and keep them around in case you need repairs. However, if you had done that, you probably wouldn't be reading this, so your Plan B option is to check with the contractor who installed your siding and buy what you need to replace the damaged panel(s). If your siding isn't more than a few years old, the new piece should look just fine.
What if you don't know who installed your siding or what brand / color it is?
You can snip a small sample from an inconspicuous place on your home and take it to a local contractor siding supply for a match. However, understand that the older your siding, the greater the chance of vinyl siding colors fading or being discontinued. If that's the case, and you can't find a match, there is a service called ITEL (formerly SidingMatch.com) that will match your siding for $140 if you send in a sample.
What if your siding has faded substantially since you installed it?
First, check your siding warranty and see if the extent of fading that you have experienced is covered. If it is not, you have a couple of options. If the damaged spot is very conspicuous, you can remove a panel from the back of your home and use it to replace the damaged section, then hang the new panel in the more hidden location. Or, you may be able to use a vinyl siding restorer to freshen up the faded surface before installing the new panel. Finally, you may be able to have the new panel painted to match the faded surface with special paint for vinyl siding.