Color accuracy is a big big topic. There are so many factors which affect the perceived image. The safest method to get the best out of our monitors is called monitor calibration and is a process with a use of a colorimeter or photospectrometer (better) to bring your colors, brightness, contrast, hue, saturation, gamma e.t.c. close to reference. Naturally a use of a software like Calman is necessary to complete the task.
Here's a good test from X-Rite:
I used to do well on the test and luckily i still do..:)