The dative case shows that a noun is indirectly affected by the action of the sentence - the "indirect object". (English can indicate this function by putting the indirect object before the direct object. e.g.: George gave the girl the ball.)

In Latin, the word for "girl (puella)" would be in the dative case. So the form would be "puellae".

1) To indicate the indirect object:
Puellae librum do.[I give the girl a book.]
Mihi librum dat.[He gives me a book.]

2) To indicate the person to whose advantage or disadvantage something is done:
Bene est mihi. [It is fine for me.]

3) To indicate possession with the verb 'to be':
Est mihi pecunia. [There is money to me.]

4) As agent:
Haec mihi dicta sunt. [These things have been said by me]
hoc mihi faciendum est [This is to be done by me.]

5) To indicate the person interested in the action:
Quid mihi Celsus agit? [What is Celsus doing? (It interests me.)]

6) To indicate the person judging:
Quintia formosa est multis. [Quintia is beautiful (in the eye of many).]

7) With certain verbs:
credo [believe]
faveo [favour]
fido [trust]
ignosco [pardon]
impero [order]
invideo [envy]
irascor [angry]
minor [threaten]
noceo [harm]
parco [spare]
pareo [obey]
persuadeo [persuade]
placeo [please]
resisto [resist]
subvenio [come to help]

8) With certain adjectives:
proximus ei [near (to) him]
Caesari similis [resembling Caesar]
Mihi utilis [useful to me]

9) Abstract nouns in the dative showing that which a thing serves for:
Odio sum Romanis. [I serve for a hatred to the Romans.]
Voluptati sum ei. [I serve for a pleasure to him/her.]
Milites auxilio misit. [He sent the soldiers to be a help.]