A processor upgrade can be a massive performance boost to any system. Like other complex systems it will be held back by its slowest component. Even given that restriction a processor upgrade can be a worthy venture.
The first step is to identify your own motherboard. You can use software tools like CPUID to identify your board, or you can open up the case and note the numbering on the board itself. Typically found between the expansion slots but sometimes elsewhere, you can then run these numbers through a search engine and figure out what you have. Make sure that you bios is up to date as well. After you do this you need to check for compatible processors. Most motherboard manufacturers will have CPU support lists for their motherboards available on their websites. If it is a manufacturer’s pc like an HP or Gateway you may need to dig a little harder.
As a rule, processors of the same family will work in the same motherboard. Core 2 6300 and a Core 2 6600 should literally be a plug and play upgrade. When you go to other families or different configurations, like a core 2 7300 or a core 2 quad 6600 you might run into more problems. You need to be wary of the heat output and make sure your heat sink can handle the new processor as well as the motherboard.
If you are using a retail PC you might get to the point where you can’t find a support list for pc’s and you are looking at not being able to upgrade. At this point, check and see if other version of that chipset in an aftermarket board like a Gigabyte or an Asus can support that processor. If they can, go on Google and search for other models of your pc and upgrades with the processor you are after. If you can find other people who have successfully upgraded to that processor odds are you won’t have any problem with it as long as you are running the same bios and version of the board.
If you cannot find anyone I would most likely decide not to try the upgrade, but that is your decision. Be aware that most retailers won’t take cpu’s back once they have been opened. This leaves EBay for you to try to make some of your investment back if you decide to purchase and it does not work.