If it's not a laptop, CPU (processor) plugs into a socket on the motherboard, so to a limited extent may be swappable for a faster one, but you won't be able to go up much in speed before you find you are into another range of processors that are incompatible, and then you need another motherboard and almost certainly different memory, and there's no guarantee there won't be further compatibility issues, like needing a different type of graphics card (various flavours of AGP (old) versus PCI-E (new)) or hard disk (IDE vs. SATA) depending on how old the old one is.

So you may be left with a complicated job and nothing left of the original but the case...