Let us discuss all those questions that we have concerning writing. Pure writing answers.
Show don't tell is when you don't describe a character trait but let the reader discover the trait by seeing the character an action.
John was very anxious
John paced through the room then he sat down again. After looking at his feet for a couple of seconds he stood up and started pacing again.
John is smart
John could see the solution immediately, it was simple really just a matter of approaching the problem with a fresh perspective.
These make your character a lot more believable AND makes it more real for the reader. Things like "smart, anxious, strong, ..." those are all relative. Just because you, as a writer, consider smart does not mean your reader will.
I hope this helped!