What word should I use to refer to myself? (I am a young girl)
Wikipedia has a list of Japanese personal pronouns which indicates formality and gender information.
Depending on whether you want to use a gender neutral word or not, and what setting it is, you could use any of the following:
わたし（neutral） - In formal or polite contexts, this is gender neutral, but when used in informal or casual contexts, it is usually perceived as feminine.
わたくし（neutral） - The most formal polite form.
われ（neutral） - Used in literary style. Also used as rude second person in western dialects.
ぼく（more male than female） - Used when casually giving deference; "servant" uses the same kanji. (僕 shimobe), especially a male one, from a Sino-Japanese word. Can also be used as a second-person pronoun toward children. (English equivalent – "kid" or "squirt".)
あたい（female） - Slang version of あたし atashi.
あたし（female） - A feminine pronoun that strains from わたし ("watashi"). Rarely used in written language, but common in conversation, especially among younger women.
うち（mostly female） - Means "one's own". Often used in western dialects especially the Kansai dialect. Generally written in kana. Plural form uchi-ra is used by both genders. Singular form is also used by both sexes when talking about the household, e.g., "uchi no neko" ("my/our cat"), "uchi no chichi-oya" ("my father"); also used in less formal business speech to mean "our company", e.g., "uchi wa sandai no rekkaasha ga aru" ("we (our company) have three tow-trucks").
You can also refer to yourself by using your own name. That would be informal and sound a bit childish, however.