Nothing could be simpler than using filters. Just screw one on to your lens and you are on to a winning picture. Or are you?
Naturally you always put a skylight or UV on your lens for protection. When using other filters remove the skylight filter first as 2 or more filters can cause vignetting (darkening) in the corners of your image. Check your LCD to see if this is the case.
A whole range of filters are available for black&white images. They are used to increase contrast and range from yellow, orange and green, to red. Their effect is to add more contrast to skies or to influence the way certain colors are reproduced in B&W images. They are unsuitable for color photography however.
When using a polarizer with wide-angles and large areas of blue sky, you should be aware of uneven polarization across the sky, where some parts are a deeper blue than others. Adjust the polarizer and take several shots to check which setting works best.
With autofocus cameras use a circular polarizer instead of a linear one. This has nothing to do with the filter shape but with the alignment of the polarizing material. The wrong one can fool your autofocus or influence exposure metering.
When using graduate filters avoid small apertures of f16 or f22, as the dividing line can become clearly visible while larger apertures will make for a smooth graduation.