Deductive vs Inductive Reasoning

Deductive
 When a person uses deductive reasoning they are coming to a conclusion based on well known generalizations.  This type of reasoning starts with a limited number of simple statements then leads to more complex ideas that build upon the initial statements.  Using the first statements as a foundation, a person can then form more complicated principles and ultimately prove them.  Deduction is basically the direct application of knowledge in order to discover new knowledge.

Inductive
 Using inductive reasoning takes events and turns them into generalizations.  It creates general principles through circumstantial evidence.  It moves from an individualized observation of an idea towards forming a generalized opinion. 

Inductive arguments provide us with new ideas and thus may expand our knowledge about the world in a way that is impossible for deductive arguments to achieve. Thus, while deductive arguments may be used most often with mathematics, most other fields of research make extensive use of inductive arguments.

This is the link to an interesting and clear article on it:
http://www.nakedscience.org/mrg/Deductive%20and%20Inductive%20Reasoning.htm