Please take this as intended - to help you improve.

First, http://www.openoffice.org/ - please go download that program and please utilize the spell-check feature before publishing a story. From a reader's perspective, it is extremely difficult to read a story when the words are frequently misspelled, generally because I have to stop and figure out what is intended.

Though this particular sentence only demonstrates a need for a possessive apostrophe, spell-check would have caught the error for you.

After a little talk, Kirito held Lizabeths hand and they both fell asleep.

There is also an added grammar checker that you can download with that program (it is also free which is very beneficial). I don't guarantee 100% accuracy, but it could certainly aid you with issues such as misplaced commas:

Liz and Kirito were in a hole because the dragon that eats crystals, saw Lizabeth and went after her.

That sentence doesn't need a comma. This is a basic outline of when commas should be used:
http://grammar.ccc.commnet.edu/grammar/commas.htm

Regarding style, this paragraph:

Lizabeth woke up with a start, she was having a dream about her real life and the last time she was with a boy like Kirito. She moves a little and realizes that she is still holding hands with Kirito. Blushing a deep red, she slowly lets go and puts her almost frozen hand in the sleeping bag. Looking up to the beginging of the hole, she saw many stars and gasped when she saw a shooting star.

It reads very much like a 'to do' list. If I were to alter it in order to help the story flow more freely, I might suggest

Lizabeth awoke, startled to find she was still holding Kirito's hand. She blushed deeply as elements of her half-remembered dream returned to her. Holding his hand had brought to mind the last assignation she had enjoyed. As her relationship with her companion had not developed to that stage, she found herself highly embarrassed by the turn of her thoughts, gently disentangling her fingers from his as she released his hand. The cold air quickly dissipated the heat from his touch, causing her to shudder.

As she stared at him in longing, a flash of light through the opening in the ceiling of the cave caught her attention. She gasped, her breath visible in the frigid air, as she saw the meteor streaking across the sky. She whispered under her breath as she stared at the trail of flame lighting the sky. Her noises woke Kirito, his eyes wide as his body tensed in preparation of attack.

Rather than listing the elements I want the audience to notice, I've described them, drawing my reader into the tale more fully and causing them to develop a greater affinity with the characters.

Now this, since I just finished watching Men in Black, struck me as funny.

Lizabeth sloly unzips her sleeping bag and crawls into Kirito, while he gets out

As I said, I just finished watching that movie, so "Kirito-suit" came to mind. I realize that's not what you intended, but it is a very good example of an area where you could seek improvement. In addition to the misspelling, I understand you intended to indicate her proximity to Kirito. So either she is curling her body into his, or she is crawling into his sleeping bag. The exact meaning is unclear, and this is why I generally suggest one enlist the aid of a beta.

This sentence:

Just wait Kirito, once we are out of this game, I am going to find you and friend you.

makes me think of Facebook with the verbiage used.

I do hope that you will consider my suggestion of obtaining a beta. At the very least, a read-through of the material should help you to catch some basic issues. Utilizing the spell-check feature in the word processing program I recommended will also benefit you.

Happy writing.
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