With the exciting appearances of both Comet C/2011 L4 PANSTARRS and Comet C/2012 S1 ISON expected to happen during the year 2013, observers around the world will be anxious to relate what they see to other amateur astronomers in a meaningful way... and one of these ways will be reasonably judging the size of a comet's coma and tail.
First let's begin by explaining comet "parts" and how they appear. The body of a comet is divided into two distinct regions - the coma and the nucleus - and not always will both be seen at the same time. While a comet is distant, its coma is basically the only thing visible. It will appear as a soft, fuzzy contrast change, somewhat similar to an unresolved globular cluster or small elliptical galaxy. Because a comet can masquerade as a deep space object, it is always very important to be sure of its position. (Small wonder Charles Messier's famous list of objects that weren't comets became so popular!) Because the nucleus of a comet is inherently small, it doesn't become visible until the comet nears Earth. When the nucleus makes its appearance, it could show as sharp and bright - or may just appear as a more concentrated region. The coma around it will continue to be hazy in appearance, but need not always be regular in shape. Be sure to watch for changes not only in size, but in appearance as well, over a period of time.
The next major part of a comet is its tail. Thanks to the solar wind, the tail will always point away from the Sun. For example, if a comet is making a morning appearance, the tail will appear to be roughly headed west? or if the comet is viewed just after sunset, it will be approximately aimed east. The tail may also appear in two sections. The most common tail appearance is the dust tail - created from the sandy, rocky volatile ingredients of the comet's nucleus. These particles stream away from the comet's body and are illuminated by sunlight and may have a slightly curved appearance. The other section of a comet's tail - the ion tail - can have a slightly blue tint and is formed from the gases flowing away from the comet's nucleus. The ion tail will always point directly away from the direction of the Sun.
Now that we understand the parts of a comet, it's time to be able to make a rough estimate of their size. When viewing through a telescope, try this simple trick: observe an easy deep space object and compare them in size. For example, you might wish to choose a globular cluster such as Messier 3. It spans around 18 arc minutes in size. Compare it to the comet. While you can't place them side by side, it will give you a rough idea. Another suggestion is to determine how many arc minutes your eyepiece reveals. For example, if the full Moon just fills the field of view, your eyepiece covers about 1/2 a degree of sky - or 30 arc minutes. If the comet is covering about a third of that area, its approximate size would be 10 arc minutes. The same holds true of judging the length of comet's tail using the eyepiece. If it extends for two eyepiece fields of view, then the tail would have an approximate length of 60 arc minutes - or one degree.
When using binoculars, judging size isn't difficult if you use your binoculars specifications. Most common binoculars cover between 5 to 6 degrees (5° to 6°) of sky - and your binocular manufacturer should be able to provide you with a specific number for your model. Simply make sure your binoculars are steady and estimate! For unaided eye observing, the principle is roughly the same. If you hold your hand at arm's length and make a fist, your fist covers about 10 degrees of sky. Your average thumb length is about 3 degrees and the width of a single finger is about 1 to 1.5 degrees.
While these aren't scientific measurements, being able to judge the approximate size of a comet's nucleus and tail is a great way to communicate what you see to your fellow amateur astronomers. Would you rather say; "I saw Comet ISON last night." Or "Comet ISON was great last night! It had a bright, sharp nucleus and a coma that was about 15 arc seconds across. The dust and ion tail stretched almost two degrees of sky!" It's great fun to learn and you can do it!