You will find further discussion about the attributes of polarising filters in 'part 7 of Composition Design', and some mention of neutral density (ND) filters, but I thought it would be better to expand on the subject by including a chapter based entirely on that subject.
Many digital SLR cameras, as well as some high range compacts, have a built-in filter option, however, I still prefer the old fashion way of doing things and if you are the same, then I hope this will be of some use to you.
I for one prefer to use the 'Cokin' brand, "P" range of filters and/or their attachments. I use 'Cokin' because I find they are most suited to my style of photography. However, all my lenses are fitted with 'Hoya' screw-on UV filters and I also use 'Hoya' screw-on polarising filters. I have found, for the sake of argument and for what I do, the 'Hoya' screw-on circular polarisers are more effective than the 'Cokin' polarisers, but that's just me.
By the way, for all there is said about UV filters, it has been proven that they don't really reduce haze in photographs. You can try the exercise for yourself if you like. Take one photo on a hazy day with the UV filter fitted and another one without, and I'll bet you will not be able to see the difference.
The main reason I keep a UV filter attached to my lenses, however, is to protect the front element of the lens from scratches, fingerprints, dust, sand and salt spray. The filters are obviously cheaper to replace than a new lens.
With the 'Cokin' range, you start with a matching size adapter ring which screws directly on to the thread on the inside front of your lens. The flexible plastic filter holder then snaps onto the outer part of the adapter ring, so you only need purchase the adapter ring that suits the lens you use and not separate filters for each lens.
It is advisable when using other filters, to remove the UV filter. It is best not to use a multiple of filters on your lens at one time. The more glass you have on your lens, the more chance you will have of getting lens flare and you may also suffer a loss light and definition.
More on filters and their effects (from the 'Cokin' range)
This filter can be used to enhance a sunset or sunrise photography or in black and white photography, it will also enhance foliage.
This one also enhances sunsets or sunrises and with black and white photography it will darken the sky and water and increase contrast in sunsets. It will also reduce haze and is known to boost texture in surfaces such as snow, sand, stone, wood, etc.
Greatly increases contrast in sunsets and sunrises as well as silhouettes, etc. Used with black and white photography, it will really darken blue skies and will also increase contrast in sunsets, enhances texture and will reduce haze from landscapes.
This is a dark filter and when used with sunset photography it will bring about a dreamy green tone. It can also be used to lighten the foliage in trees, etc.
This being much lighter in colour, will give a moody and mysterious look to landscapes and sunsets, but when used with black and white it will give a more natural look to foliage.
'Blue (80a) #020'
Reference to black and white photography only. This filter absorbs yellow as well as green and red; it will increase the appearance of haze in landscapes and will lighten all blue areas like sky and water.
'Neutral density (ND)' filters
ND filters are grey in colour and come in varying densities of -1, -2 and -3 stops (ND 2x #P152, ND 4x #P153, ND 8x #P154), also an extreme 7 stop is available that will cause pedestrians and moving vehicles to vanish into mere blurs.
They are very useful for darkening a bright sky or slowing shutter speeds when necessary. For instance, depicting the movement in moving objects and creating that dreamy, moody appearance of rivers running over rocks, waterfalls, etc.
Although they are grey, they will not cause any loss of colour in your subjects.
Or grey grads, as they are known. G1 #120, G2 #121. Only half of the filter is grey and the other half is clear.
It will add drama to an overcast sky and is very useful in landscapes or cityscapes, where you want to reduce the brightness in only half the scene.
There are also other coloured grads available for different colour effects.
These are known as the 81 series filters. For instance, 81B #027, 81D #035, or 81EF #037. These filters are used to add warmth to an otherwise grey or overcast scene. Also, an 81B or D is good for enhancing skin tones in portraiture.
These are in the 80 series and are blue in colour. You can use them to create a cool, moody appearance to a seascape or increase colour in blue haze in mountain scenery. They also come in varying strengths.
There are also a myriad of special effects filters available, too many to mention here, but it's worth dropping into your local camera store and asking for a brochure on filters.
You can use a graduated tobacco (T1 #124), coupled with an (81B #027) warming filter to add drama and colour to an otherwise dreary scene.
A polarizing filter will work at its optimum best when used at 90 degrees to the sun. In other words, the sun's path is from East to West, so the nearer you are facing North or South, the more functional your polariser will be. They are also best used early to mid-morning or mid to late afternoon.