As you know from the Intro, in German, there are four cases. Three are used often. The first, Nominative Case, you learned in Lesson 1. It covers the subject, and the predicate noun (in "He is (noun).", (noun) is the predicate noun). The second, the Accusative Case, you will learn now. It covers the direct object and the object of several prepositions. The third, the Dative Case will be taught later on. It covers the indirect object and the object of many other prepositions.
Note: The Accusative Case and Dative Case are identical in English; that's where the extra case comes from.
Articles
Masculine Feminine Neuter Plural
Definite Article den die das die
Indefinite Article einen eine ein -eine*
* The indefinite article for plurals is non-existant. However related words, such as possessives and the kein- words that you will learn later this lesson, will end in eine for plurals.
In the articles, the memory hook for accusative case is "Der goes to den (pronounced "dain") and the rest stay the same.". The masculine indefinite article goes to einen, and everything else stays the same there. Therefore above, der Hamburger goes to den Hamburger and ein Hamburger goes to einen Hamburger when the hamburger is the direct object, such as in "Er hat einen Hamburger." ("He has a hamburger.")
If you are getting confused, it's fine. This topic is one of the hardest for English speakers to grasp. Here are some solutions:
To find out the case of something, first find the verb. The verb rules the sentence. Everything revolves around it. Next you find the subject of the sentence. The subject is the thing/person that is doing the verb. The subject is always in the Nominative Case, so it takes on the der, die, das, die, or ein, eine, ein.
Now you look back at the verb. If it is a being verb (am, are, is, etc.), the next noun after the verb is the predicate noun. An easy way to figure this out is to write an equation. If the verb can be replaced with an equals sign (=), then the following noun is a predicate noun. If it can't be replaced by an equals sign, refer to the next paragraph. The predicate noun is also always in the Nominative Case, so the same rules apply to it.
Ich bin ein Junge.
Sie ist eine Frau.
If the verb of the sentence is an action verb (playing, throwing, making, eating), find what the subject is doing the verb to. For example, if the verb is "makes" (macht), you look for what is being made. That is the direct object. The direct object is always in the Accusative Case, so it takes on the den, die, das, die, or einen, eine, ein.
Sie haben den Cheeseburger.
Habt ihr einen Salat?
The indefinite articles, when you just look at their endings, go -, e, -, e for nominative case, and en, e, -, e for accusative. This can be memorized as "Blankie, Blankie, Any Blankie."
Remember, between nominative and accusative, the only third-person change is in the masculine form.
Pronouns
The pronouns experience a much bigger change than the articles. This is also true in English, as the articles (a, an, the) do not change ever, but I goes to me, we goes to us, etc.
Not everything is the same, though. While me is mich and us is uns, the second and third persons undergo different changes. In third person, as in the articles, the only change is in masculine singular.
Following the "der goes to den" rule, er goes to ihn when in the accusative case.
The second person in English never changes. In German, du goes to dich and ihr goes to euch. Sie, the formal version of either, stays the same. Remember, Sie (2nd person formal) and sie (3rd person plural) only differ in their meanings and the fact that the former is capitalized and the latter is not. This stays true throughout German grammar.
Here is a tabular representation of the above.
Person Singular Plural
English German English German
1st me mich us uns
2nd you dich you (y'all) euch
3rd him, her,
it ihn, sie, es them sie
Antecedents
Note: This is just a quick lesson in English grammar applied into German. If you already know all about antecedents in English, skip the first paragraph.
When using a pronoun, you have to know what it is for it to work. There are some rare exceptions, such as in mysteries or drama, but otherwise this is always true. Sometimes in dialogue this is taken care of by pointing or making some other gesture, but most of the time, the pronoun modifies something already mentioned. The object/person mentioned earlier that turns into a pronoun later is called the antecedent.
In German this is very useful. You can't simply say 'it' anymore. Many food words are masculine and feminine, and when you turn them into pronouns, they turn into 'he', 'she', 'him', and 'her', not always 'it'. For example, the sentence "The cheeseburger tastes good. It's very crunchy." turns into "The cheeseburger tastes good. He's very crunchy." Note: You will learn how to say this in German later in this lesson.
Why is it "he"? This is where the antecedent comes in. Because there are foods that are masculine and feminine in German, you can't assume the 'es'. You have to look back at the previous sentence, at the antecedent, der Cheeseburger. "Der Cheeseburger" is replaced by er (since it is the subject, and therefore in Nominative Case). Therefore, all you need to know are these connections: der/den-er/ihn, die-sie, das-es, die-sie.