First things first.
Before we begin, we should define what an argument is, and what one means by argument analysis.
An argument consists of both a claim (which is called the conclusion) and reasons to accept the claim (called the premises).
To analyze an argument is to determine whether the argument actually gives good reasons to accept the conclusion, and to provide reasons why it does or does not provide good grounds to accept the conclusion.
With these definitions in mind, we will now discuss some fundamental steps in argument analysis.