So how do you go about calibrating your monitor? First of all, take a look at your monitor settings - can you alter the colour settings of your monitor? Along with contrast and brightness, you will probably have access to colour temperature and more often than not, access to the individual RGB settings of the monitor (sometimes stated as a "User" option on the colour temperature menu). The colour temperature has an effect on the white point of your screen. Usually you have a selection of defaults - around 9300K, 6500K and maybe 5000K. 9300K gives a blue (cool) cast to the white, whereas 5000K gives a yellow (warm) cast to the white. 6500K (or thereabouts) tends to be the most neutral, and is the default choice for sRGB image editing - it's best to set your monitor to this (many monitors will initially be set to 9300K).

Also, check to see if you have access to changing the individual RGB settings - if you do, then you can change the colours (which may also alter the brightness of the screen). It's best to leave these alone, and stick to the 6500K setting for now, but they can be useful later on for more advanced calibration.