An Argument is a series of statements used to persuade someone of the conclusion; or your "claim". We call your "claim" the thesis. Premises are statements that directly support the conclusion.

A simple thesis has two premises and a conclusion;

In a complex argument, the conclusion is supported by its three premises, but each premise itself can be supported in a number of ways:
 

• •Supporting Arguments - such as definitions
• •Assumptions - comparable to a premise and usually not used as support as it is a restatement of the premise. Some things we assume such as the sun will rise everyday.
• •Evidence - statistical studies, historical information, physical evidence, observations, or experiments, and eyewitness accounts
• •Authority - scientists, psychologists, authors,
• •Explanations and anecdotes - examples and quotes from a literary source, personal experiences, stories told by others who are not necessarily authorities.

These are called your "proof" - Some proof has more credibility and is more convincing than other proof. There is a hierarchy of evidence or support. Some proof is verifiable and some is convincing. Facts are often in the category of verifiable while support given by an authority or an explanation are only as convincing as the authority or explanation. Evidence is not always a "fact" and can always be disputed. Examples of evidence are statistical studies, historical information, physical evidence, observations, or experiments, and eyewitness accounts.
 

Your premise (or thesis) will be a claim with three supporting opinions. You break down your thesis in order to be able to prove your claim.