How do you know if an argument is valid, formally valid, or sound?
A great question!
In an argument (not meaning a fight, but rather the proposal of a point) a person's statement has a valid logical form if it follows an appropriate structure: All dogs are green, I am a dog, therefore I am green.
It is formally valid if the statement "follows." It doesn't have to be true, it just has to correctly follow the logical formula. For example, All dogs are green, I am not a dog, therefore I am not green. It has the parts of valid logical form, but doesn't follow. I might be something else that is green. It's valid in structure but not formally valid.
To figure out if an argument is sound, you have to determine if all the parts of it are true. In a way, it's passing the filter of "common sense." For example, if I say Everyone driving a Prius has 11 toes, you are driving a Prius, therefore you have 11 toes. This is formally valid because if the first statement is true, and the second is true, than the conclusion must be true as well. It is not sound, though, because the premise (that everyone would have 11 toes) doesn't make any sense.
That's why it is so easy for people to sound like they know what they're talking about when they don't. What their saying is formally valid, but not all the premises are true.