Deductive reasoning starts from a general theory and then works towards a specific hypothesis that can be tested. The testing of the hypothesis then either confirms or rejects the original theory. Inductive reasoning starts from a specific observation and works towards a general theory.
Deductive reasoning can be very simply described as: if A then B. It involves making a statement that the person doing the reasoning thinks may be true. Deductive reasoning is the kind of reasoning that is used in a setting such as a high school science class where the students come up with a hypothesis and then test that hypothesis for themselves. The scientific method is a form of deductive reasoning.
Inductive reasoning takes observations and then uses those observations to come up with a general theory. If a person reaches into a bag of marbles and pulls out a handful of all blue marbles, using inductive reasoning would lead the person to believe that all of the marbles in the bag are blue. Inductive reasoning is the kind of reasoning that detectives, including the fictional Sherlock Holmes, use. They find the clues, make observations about them and then come up with a theory of what happened.