“Argument” is a flexible word. An old married couple hurling insults at one another can be said to be having an argument. One might say that Donald Trump is himself an argument for abolishing the Electoral College. One might follow the John Cleese character in the Monty Python skit and say that merely contradicting what someone says is an argument. For my purposes, I will limit the term to something very close to what the Michael Palin character said in the skit: “an argument is a connected series of statements intended to establish a proposition.”
Somewhat more specifically, I’ll say that an argument must have the following elements. First, an argument must have a conclusion: a statement about the world claimed to be true. This conclusion is said to logically follow from statements that are simply accepted without further argument; the latter statements are the premises of the argument. An argument is logically valid if the conclusion really does follow logically from the premises. An argument is sound if it is valid and its premises are true. Thus an argument can be a bad argument in more than one way: one or more of its premises might be false, or its conclusion might fail to follow logically from the premises.
Note that in my narrower sense of the term “argument”, people who are simply hurling insults would probably not count, for there is no attempt to establish conclusions by asserting premises from which the conclusions logically follow. Donald Trump, being a human being rather than a statement of any sort, does not count as an argument for anything in this sense.
I will very often lay out an argument in numbered steps to make its structure more clear. Here is a simple example of a bad argument:
(1) Donald Trump is a very stable genius. [Premise]
(2) Some very stable geniuses have small hands. [Premise]
(3) Donald Trump has small hands. [1,2]
This argument is bad on several grounds, although its conclusion is true. The first premise is dubious, to say the least. The second premise is presumably true; I’m not sure who out there counts as a very stable genius, but I imagine that at least some of those people have small hands. But the conclusion in (3) does not follow logically from (1) and (2). Even if (1) were true, the argument would be invalid.