I often get asked about filters so here is a quick guide on what are the most commonly used types of filters available and why you might want to use them. So starting from the left and moving clockwise....
UV (also called Skylight) filters
Often when you purchase a lens you are prompted to buy one of these too.
These are circular filters that screw onto the front of the lens. Other filters can be applied on top of them. With modern technology these are now less about reducing the effects of UV in your images and more about providing protection for your lens. Better to scratch one of these than the lens itself. They are now relatively inexpensive.
These come in both round and square options. I prefer the circular option as they are easier to use and adjust - they are usually referred to as circular polarisers. Square filters are more commonly used in conjunction with Neutral Density filter systems (see below).
Like the UV filter it screws to the front of your lens. You can then adjust the effect of the filter by rotating the lens.
Use one of these to help reduce glare and reflections and to saturate the colours in your photos.
ND Grad filters
These filters help you balance the exposure of ground to sky so are usually used for landscape type images. The filters are darker at one end and clear at the other. Placing the darker end over the sky in your image means you are able to maintain the detail in the sky that might otherwise be lost.
There are two types of ND Grads - soft and hard. This is about the type of transition from dark to light. Hard filters are best where you have a distinct horizon line - a seascape, for example. Soft filters allow a gradual transition which is better for landscapes with 'uneven' horizons with trees, buildings etc.
They come in different strengths - eg ND4 (which is a good one for most uses) However, if you are shooting in much brighter light you may find that you need a much darker strength such as an ND8.
Because you are lining up these filters with a horizon you need to use a square system. This means purchasing not only the filter but a holder that fits your lens.
These are the filters that enable you to shoot long exposures during daylight hours to blur water etc. Unlike the ND grads these are dark filters that stop the amount of light entering the lens and, therefore, prevent overexposed images.
These come as both square and round filters. The advantage of the square system is being able to stack in the holder more than one filter including polarisers and the ND grads.
How strong a filter you need depends on the amount of light you are shooting in. An ND8 is a good choice for most conditions. For extreme slow shutter speeds and very bright conditions you will need filters such as the Lee 'Big Stopper'.
All of these are widely available from photographic retailers and sites such as Amazon. To get the best results don't necessarily go for the cheapest option - the optical quality of polarisers and the ND filters (both types) will affect how successful your image is.
Second hand ones are often available but do make sure they are in great condition and buy from a reputable source.