The Dative case in Latin has a number of important jobs, which you should aim to learn bit by bit as you come across them in your reading. Some are very straightforward, others less so. My advice is to keep the basic formula “dative = to/for” in your head, and then be able to think on your feet. Sometimes you’ll be able to translate correctly without knowing the name or category of the particular dative you’ve met. But grammarians like to give things names, so let’s look at some of them.
(i) Dative of Indirect Object. When you give something to someone, as in English, you need a dative. In the sentence “I’m sending a letter to you,” the letter is the direct object, and you is the indirect object. In Latin, mitto epistulam tibi.
(ii) Dative of Possession. It is quite common in Latin to say “there is X to me” as an alternative to “I have X.” So you can say habeo duas gallinas “I have two hens,” or sunt mihi duae gallinae, literally, “there are two hens to me.” You’ll see this very often when people give their names: nomen mihi Claudia est (“My name is Claudia.”)
(iii) The Predicative (or “double”) Dative. This is a construction that isn’t so recognisable from English. A predicative is something that describes the subject of a sentence, a verb for instance. “Seán (subject) walks (predicate)’. So a predicative dative is a dative used to describe a subject. You’ll normally find it with the verb esse and a second (hence “double”) dative, telling you who is involved in the action. It’s easiest to grasp this through examples. As usual, starting with a literal translation will help.
es auxilio mihi: “You are for a help to me,” then “You are a help to me.”
ea, quae usui sunt mihi: “… those things, which are for a use to me,” then “… those things that I find useful.”