A Brave Knight

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There once was a boy, who lived a long time ago, on the edge of a kingdom named Myf. He sat all day on the streets and polished shoes for travelers. His mother made clothes for the queen and the princess, and his mother made fancy clothes for him too. He loved fairy-tales. Sometimes he would draw his polishing rag and pretend to slay a dragon.
One day, the sun was blocked by a fire breathing dragon. No one could see. Then everyone could see again, because the dragon flew over to the castle and grabbed the princess. He flew away to a dark cave. Everyone was sure the princess would die. The king and Queen cried and cried. They sent out many knights with shining armor, which the boy wanted to be. They never came back.
So he went. It seemed silly, but he was going to save the princess. He went out with a few coins and stopped at the blacksmith’s hut to get a sword and a shield (just so the princess wouldn’t think he was a fool and so he could slay the dragon). His mother had said to him one day, “Darrel, I think it would be a wonderful idea for you to go save the princess.”
Darrel (the boy) shuddered at this thought. He wasn’t brave. Well, he had gained some courage from reading the fairy tales in the library, but that wasn’t bravery. He would much rather sit on the street and make his salary polishing shoes. Plus he would also get a ten coin week allowance. But there he was, a boy with a sword and a shield, and a loaf of bread in his pocket, stepping into the dark forest.
Darrel wandered all night long, looking for a dry place to sleep, and then he found a large boulder where he could take a nap. A new day was dawning; he could not get a full night’s sleep now.
He suddenly awoke. Then he saw a large cave in the distance, just the perfect place for a dragon’s den. He slowly got up and tiptoed to the cave, his sword and shield ready. He stepped in the cave and a girl in a wrinkled garment ran out of the cave. She said, “Finally, all these knights are getting boring.”
A dragon stepped out of the cave. It flew up and made Darrel back away, to the edge of the cliff. He was about to slay the dragon with his sword, when the dragon breathed out fire and made Darrel back off the cliff. Darrel’s sword plunged into the hard rocky cliff. He managed to climb up and throw his sword at the dragon. It landed with a nice big thud.
The princess helped Darrel into the cave. He took the loaf of bread out of his pocket before he sat down, and offered her a piece. She nodded, said “Thank you.” (Her voice was very weak) and took the piece of bread. He took a piece for himself. They chowed down in silence.
The princess had started getting grumpy. Darrel was about to lead the princess (he found out her name was Leah) to the kingdom of Myf and back to the castle, when his map blew away in the wind. That was her trigger. She was going crazy. She had been trapped in a dragon’s cave for a week with nothing to eat but a slice of bread. But reader, I’m sure anyone would go crazy like that. She walked away from Darrel and dug her toe in the dirt. She frowned and crossed her arms.
Darrel yelled, “Come on Leah! We’re going to be here forever if we don’t get moving.”
“No.”
“I saved your life, and now you aren’t going through the woods to Myf?”
“Yeah,” she said, and jumped off the cliff into the ocean.
Darrel dived in right after her. He swam with her on his back. He pushed her onto shore, and said to her, “What are you thinking? I’m your servant or something?”
She replied, “Thank you. I didn’t jump off the cliff by the way. I slipped.” She got up and said, “ Let’s go!” and ran into the forest. Darrel didn’t have to be told to follow her.
When it became night, they came to the edge of the forest and stepped into the lighted Myf. They ran to the castle. The queen looked up with red eyes from crying and saw the two kids in the doorway. She pushed her husband up and said, “They’re here.” He looked up and saw them. They ran to Darrel’s house. His mother gave them new clothes, for the ones they wore now were tattered. She whispered in Darrel’s ear, “See, I knew you could do it.”
They ran back to the castle. The king got up and said, “You have saved my daughter. The kingdom of Myf gives you appreciation. We will see to it that you will marry my daughter. I will also grant you one wish.” Darrel and Leah smiled at each other.
“I want to own the library.”
“Done.”
The librarian did not care and said, “I have been waiting for someone like you to come and take this library. I hate reading anyway. My aunt Sheila gave it to me for my birthday.”
Darrel and Leah sat all day in the library reading while Darrel’s mother made a spectacular dress for Leah and a wondrous suit for Darrel. Darrel was nervous about becoming king, but reading the fairy tales calmed his nerves.
He read:
The prince slayed the dragon and got on his horse with the princess and they got married and lived happily ever after.
THE END
But that wasn’t the end for him. Darrel and Leah still had a streak of mischief in them, so at their wedding they looked at each other and nodded. “FOOD FIGHT!” They smashed cake into their faces and they laughed the night away.

Your writing style is a lot like the way someone would tell a story around a campfire. That is, it would work well told verbally. Unfortunately, when someone reads a novel or even a short story, they expect a lot more detail and depth than that. The same sort of stuff as in my other reviews of your work applies here.

As for the story, you really need to put something else in there. A boy rescuing a princess from a dragon is about the most cliche plot there is. That doesn't necessarily mean don't use it. It can be a very good plot - Shrek is based around that plot and it is in my opinion THE best animated movie ever. The reason it still works is that there's a unique twist on the plot, namely the "brave knight" being an ogre and his "noble steed" being a talking donkey. If you want this to stand out from the generic slaying the dragon story you'll need to put a fresh spin on it.

Now down to some more specific things.

His mother had said to him one day, “Darrel, I think it would be a wonderful idea for you to go save the princess.”

Where's his mother's maternal instinct? She's basically telling her son he should go risk his life rescuing some sheila (excuse my Australianism). My mother would never ask me to risk my life for anything, and she'd go out of her way to stop me if I were to do such a thing. Mothers have a strong protective instinct for their children, and I can't imagine any real woman suggesting her son do something that dangerous, especially at his age (You don't mention his age, but since nothing romantic happens when he rescues the princess, I'd assume they're 16 at most, but I get the feeling that they're a few years younger than that).

Darrel (the boy) shuddered at this thought. He wasn’t brave.

Good. A mistake a lot of amatuer writers make is that they make their main characters perfect in every way, so it's good to see a flaw. It's much easier to relate to a character who has faults like any real human does. However, instead of telling, you could show. Show us his fear and anxiety through his actions. At the moment his actions contradict this - I mean, he jumps off a cliff with no hesitation to save the princess.

The princess's name is Leah - like princess Leah off Star Wars. I don't know if you named her that knowingly or not, but the name's taken, and people will think it's pretty cheap if you appear to be copying names from a well known series of movies (whether you knew about it or not).

The bit where she "slipped" off the cliff seems a bit - I don't know, strange. People don't usually just randomly slip off cliffs. Wasn't very believable. If you want her to fall off the cliff you'll need to think of a better way to do it. A freak gust of wind would be an improvement, but that still seems a little contrived. Something to figure out.

The librarian did not care and said, “I have been waiting for someone like you to come and take this library. I hate reading anyway. My aunt Sheila gave it to me for my birthday.”

How convenient that the librarian didn't want the library - and how unlikely. If she didn't like it why didn't she sell it earlier. Why did her aunt Sheila (gotta love that name) give her the library if she didn't like reading.

I would get rid of this part entirely. It is unecessary. Alas, your story won't have the word Sheila in it - or maybe it could. Since Leah really does need renaming...

The ending was nice, and unique.

I hope this will help improve your writing skills. Feel free to PM me if you need more help. I'm still fairly new to YWS, but I could probably answer most questions if you have any about the site. If not then a mod can. Don't hesitate to ask, we're all friendly here.