There are two general types of ways to examine arguments for soundness: formal and informal.
Formal Fallacies are errors in logic that are due entirely to the structure of the argument, without concern for the content of the premises. We can refer to all formal fallacies as Non Sequiturs. Aristotle held that the basis for all formal fallacies was the non sequitur, which is why the term is known in Latin as Ignoratio elench - or an ignorance of logic.
Informal Fallacies occur when the "reasoning" or rationale behind the specific content of a premise is illogical - i.e. the support for the argument relies on rhetoric (appeals to emotion). While these arguments also possess a particular form, one cannot tell from the form alone that the argument is fallacious.