You will need a desktop computer with a compatible GPU, stable internet connection, and an Ethereum wallet address. You can use Windows or Linux as your operating system. Windows will be easier to setup/configure for most mining newcomers.
GPU information such as Ethereum compatibility and performance can be found on Mining Hardware Comparison.
CPU mining is possible but not recommended. GPU's can hash an order of magnitude faster. CPU mining will work on our pools, but it is not officially supported.