Stress testing involves running applications which stress components of a system (either individually or collectively). Its most common uses are for diagnosing potentially faulty components or testing the stability of overclocked hardware.
See the Memtest86 guide.
There are a number of applications which can be used to test these components. Generally the same principles are followed:
If the stress testing application returns an error, or the computer freezes or restarts, then the system is not stable.
Prime95 is a favourite for overclockers. If a system is able to run the blend test for 6 or more hours, it is generally considered to be completely stable.
The blend test stresses both ram and CPU. The small FFT and large, in place FFT stress tests only stress the CPU.
Stress Prime 2004 has a handy front end for Prime95, which is not especially user-friendly. For dual core processors, the Orthos edition referred to on that page is required.
There are a few methods you can use to stress test a graphics card:
An unstable graphics card can cause freezes, restarts, a crash to desktop, or graphical anomalies (such as artifacts).
In all cases, temperatures should be monitored. Most newer graphics cards have the ability to display temperatures, and both ATI and nVidia have utilities to do this which form part of their standard drivers (and in particular on the most up-to-date drivers).
Rivatuner supports GeForce and Radeon 9 series cards, and has a number of useful functions (including overclocking and temperature logging).
Suitable maximum temperatures vary from graphics card to graphics card.