There are a zillion arguments, but not a zillion ways of making an argument. An argument can be broken into steps, each step conforming to one of a small number of types.
The Analogy argument type has two or three premises. Analogy is saying that if two things are similar in one way, they are probably similar in another way.
The And argument type can have two or more premises. It is used to connect statements together into one compound statement.
The Because argument type works “backwards”, from effect to cause. Given the situation, what is most likely to account for it?
The Cause and Effect argument type has two premises. One is a generalisation about a cause-effect relationship, the other is an event. From these, another event is inferred.
The Classification argument type requires two premises. One is a generalisation or rule, the other concerns a specific case. Using the general premise, a new fact can be derived about the specific case.
The Confirmation argument type has two premises. One is an “if A, then B” statement, and the second says B is true. This confirms that A is true. Confirmation is similar to Implication, but weaker and easier to undermine.
The Definition argument type requires two premises. One is equivalent to a definition, the other concerns a specific case. Using the definition premise, a new fact can be derived about the specific case.
The Either / Or argument type has two premises. One premise presents two alternatives, the other states that one of the alternatives is false (or true). This means the other alternative is true (or false).
The Entailment argument type has one or more premises. Entailment is the idea that one statement can ensure the truth (or falsity) of another – this is normally a matter of common sense.
The Expert Opinion argument type has two premises. One says what the expert has said. The other that they are an expert in a relevant field. The conclusion is to believe or do what the expert said.
The Generalisation argument type can have any number of premises. It is used to move from specific cases to a general statement about those cases.
The Implication argument type has two premises. The first is an “if A, then B” statement. The second either says A is true – in which case B is true, or it says B is false – in which case A must be false.
The Personal (ad hominem) argument type has two premises. One states what a person says. The other is a comment on that person’s character. The conclusion is whether to follow their advice or not.
The Popular Opinions argument type has two premises. one states what “everyone” is doing, the other is a reason to follow to crowd. People often leave the second premise unstated.
The Value argument type has two premises. One says that a certain state of affairs has value. The other states that an action will bring this about. The conclusion is whether the action should be done or not.