It is not common for Scandinavians to be able to understand Icelandic and Faroese. These languages are not thought of as part of the three typical Scandinavian languages. Some words are the same, yes, but not enough for us to be able to really understand the two languages. It is possible that the Norwegian dialect reminds of the Icelandic and Faroese. And some words are spelled the same way as in Norwegian, but many other words are completely different.
As mentioned, the two most similar languages are Danish and Norwegian. Norway was once under Denmark and this is likely to be the reason why the languages are so similar. Finnish is a language that is very different from them, due to its origin in the Eastern European countries.
Even though Swedish is similar too, there are some Swedish words that a Danish and Norwegian person cannot possibly understand unless they know them beforehand.
The main difference between Danish and Norwegian is the spelling of and pronunciation of words - the words are the same words, just spelled very slightly differently. In some cases, a certain word will be used in Norwegian and another in Danish. However, in nearly all cases, both words will exist in the other language and have pretty much the same meaning.
Example in English - tooth paste and tooth cream. Danes and Norwegians can read the other language pretty much as easily as their own. It is possible for Danes and Norwegians to read Swedish, but it requires more effort due to the greater difference.
When Scandinavians sometimes end up speaking English between themselves - instead of using one of the Scandinavian languages - it is because of the dialects existing in the Scandinavian countries. It can be quite hard for Danes to understand Norwegians as they 'sing' and Danes 'talk as if we are chewing a potato at the same time'. Depending on the region, some Swedish speaking people are easier to understand for Danes than Norwegians - because they don't 'sing'.
However, understanding each other is only a matter of practice - just like when an American person tries to learn to understand a Scottish person.