I am very confused by your use of the terms "dual" and "plural".
Are you talking about
grammatical number? If so, then your definition of "word" is very important. A word might mean a lexical item or lemma, in which case
lexical items do not have number-- "dog" and "dogs" are the same lemma. A word might also refer to a grammatical word or word form, such as "dog" or "dogs", and they do have different number.
Dual is used just like plural. When there is one of something, you use singular. When there are two, you use dual. When there are more than two, you use plural.
English has singular and plural. There are also mass nouns, which do not distinction between singular and plural, and there are some unusual plural-only words like "scissors" which behave anomalously.
There is no dual in English.
Other languages also have other categories such as trial (3) and possibly quadral (4; very uncommon), as well as "multal" (many) and "paucal" (few). For some large numbers, a different system may be used-- for example after 10 in Arabic the singular is used again. (In that case, the singular might be called a "general number", rather than strictly singular.)
The way to test these is simple. Take a simple countable noun like "house" or "man" and then ask a speaker how to describe a scenario in which there are 1, 2, 3, 5, 10, 20, 100, etc.
http://en.wikipedia.org/wiki/Grammatical_number