List two ways to check hardware and software compatibility for Windows XP?

I'm not sure about two ways, but there is one which I can tell you about. To check hardware compability is not a problem at all. You need to find out that the hardware has or has no drivers for Windows xp. If it has it means that it's compatible. If it doesn't it's still might work with drivers from another manufacture but there is a little chance. Software compability is described in help file which is usually provided with software. You might need to check software websites for more information or just google it.