How do you know when to use a relative pronoun, and which one do you use?

A relative pronoun comes almost always at the beginning of a relative clause. That's usually when you want to give extra detail about an object in your sentence. In English, this would be something along the lines of: "The car that is parked in front of the tree is green." In German, it would look like this: "Das Auto, das vor dem Baum geparkt ist, ist grün." Relative clauses are always surrounded by commas (as if they were brackets surrounding the extra information, much like this bit of the sentence now), and the verbs always go at the end of the clause. As you can see, "ist" is at the end of the sentence; here, "geparkt" is just an adjective, not a past participle. On the subject of the perfect tense, it is the auxiliary verb that goes at the end of the clause: i.e. "Das Mädchen, das an die Tür geklopft hat, ist meine Nichte" (The girl who has knocked on the door is my niece). 

The relative clause you use will depend on three things: 1) the number (is there just one, or are there many?); 2) the gender (is it masculine, feminine or plural?); 3) the case (Nominativ, Akkusativ, Dativ, or Genitiv). The relative pronouns for the first three cases (Nom, Akk and Dat) are the same as the words for "the", but they are different for the genitive case. We will go over that at a later stage, as that is something you won't necessarily need to know for A-Level, but it is handy to know once you have gotten the hang of the other three cases' relative pronouns.