Calibrate your monitor

You must be able to see all this:
-- 20 sections of equal width and different tone
-- the darkest section must be pure black
-- the lightest section must be pure white
-- there must be no hint of colour anywhere along the grey spectrum

If you don't see 20 different tones, you may need to lower the contrast.
If black is not pure black, you need to either darken the monitor or adjust the black point.
If white is not pure white, you need to either lighten the monitor or adjust the white point.
If both black and white are not pure, try to boost the overall contrast or adjust both, the black and white points.
If there is a colour cast, try and adjust the colour balance. Some software allows you to do this separately for both ends of the grey spectrum.

Once you have adjusted everything as precisely as you can, look at these test images (Red, Green, Blue):

There are 16 clearly defined patches in each strip.
If you cannot distinguish between them towards the dark end in any of the strips, you may need to lighten the respective colour, or darken the other two colours.
If you cannot distinguish patches towards the light end in any of the strips, you may need to darken the respective colour, or lighten the other two colours.
You can also try to work with saturation controls for the individual colours, if they are available in your Software.

Also, have a look at the following test images (Cyan, Magenta, Yellow):

There are 11 clearly defined levels in each strip. You will find a relationship between how these are displayed and how Red, Green and Blue are displayed.
-- If the deepest yellow patches are indistinct from each other, your darkest blue is probably too close to black..
-- If the deepest magenta patches are indistinct from each other, your darkest green is probably too close to black..
-- If the deepest cyan patches are indistinct from each other, your darkest red is probably too close to black.
Some men may have difficulties with the deepest colour patches. If in doubt, zoom in for a close look.... or ask a woman.

If you have a fairly precise inkjet printer, you can print out these last three strips and the greyscale. If your monitor settings are correct, the print should look close to the representation of those strips on your screen. Changing any of the monitor settings should have no effect on the print. So, if you can trust your printer, this is a very good indication of a correct monitor setup.

All this requires patience. Each setting has an effect on everything else. You may need to go back and forth between adjusting two or more parameters dozens of times.