How to show (without telling) - Method 1: Strong, believable dialogue
Hemingway was a master of strong dialogue. Read the following excerpt from "The Killers" by Ernest Hemingway:
"I'll have a roast pork tenderloin with apple sauce and mashed potatoes," the first man said.
"It isn't ready yet."
"What the hell do you put it on the card for?"
"That's the dinner," George explained. "You can get that at six o'clock."
George looked at the clock on the wall behind the counter.
"It's five o'clock."
"The clock says twenty minutes past five," the second man said.
"It's twenty minutes fast."
"Oh, to hell with the clock," the first man said. "What have you got to eat?"
"I can give you any kind of sandwiches," George said. "You can have ham and eggs, bacon and eggs, liver and bacon, or a steak."
"Give me chicken croquettes with green peas and cream sauce and mashed potatoes."
"That's the dinner."
"Everything we want's the dinner, eh? That's the way you work it."
"I can give you ham and eggs, bacon and eggs, liver--"
"I'll take ham and eggs," the man called Al said.
This story is almost entirely dialogue, with the barest amount of description to move the action along. Some writers wouldn't be able to pull this off because they don't have a strong enough sense for believable dialogue. However, Hemingway's characters immediately spring to life.
Notice how the dialogue includes scene details. Instead of the narrator telling us what the clock looks like when George looks at it, the characters provide the information through their conversation. They also talk about the card and menu, which are props of the scene. It isn't much, but it's enough to give us a taste of the environment.
More importantly, Hemingway uses the conversation to reveal characterization. We aren't just getting the time (which turns out to be important to the story). We're discovering that the first man is impatient and doesn't listen, while the second man is perhaps a little more observant. George's responses are straightforward, if unadventurous. He doesn't seem to frustrate easily, given how he repeats the available menu almost like a broken record. This suggests he's proficient at doing his job. We learn a lot from the rich interchange without having to be told what kind of people they are.
The result is that we, as readers, feel like we're in the lunch-room with these men, experiencing the story along with them. This is what good showing achieves.