The things you need to know are the socket type, the CPU clock speed generated by the board, and the frontside bus speed (the speed of the memory bus). Intel and AMD require different support chip sets, so you have to know which type of chip your board uses. The CPU clock speed will either be automatically set (within the limits of the board) by the BIOS, adjustable by jumpers, or will have a DIP switch.
Many older computers have data available on the Internet. Just enter the brand and model into a search engine like Google - you can generally find the specifications.
Any PCI graphics card should work in your machine, as long as drivers are available for your operating system (i.e. WinXP, Win2K, Linux, etc). A limitation would be on the amount of current required. Some high speed video boards have additional power connectors on the top edge of the board. You plug in a spare drive connector to supply the additional video power that the PCI bus cannot handle. Such video cards will say on the specifications printed on the retail box what size computer power supply is recommended.