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I'm a German native speaker and was asked to explain the difference between "einem" and "einen". I found it very hard to generalize the usage and formulate a rule of how to use those two.

Examples:

Ich habe ihn einem Freund vorgestellt.

Ich habe ihm einen Freund vorgestellt.

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2  
Are you comfortable with the difference between accusative and dative? – Tim N Jun 23 '11 at 9:22
Yes I am. Great answers – Alexander Stolz Jun 23 '11 at 9:33

2 Answers

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One should learn the proper case with each verb, but there are some general heuristics (which are, of course, not always true):

The accusative is used for the thing or person that the action is done to and the dative is used for the thing or person the action is done for.

So:

Ich habe ihm ein Keks gegeben.

The action of giving is operating on the cookie, so accusative, and he is the recipient or beneficent of the action.

Your example of introducing people is not very good because this action is usually symmetric. But if you want to analyse this particular sentence, note that vorstellen literally means "put in front of". So, you take the accusative for the person you put in front of someone else, and you take the dative for the person who is the recipient of the action.

So, if you say "Hi, Dan, this is Mia.", you have presented Mia to Dan, so Mia is accusative and Dan is dative.

For English speakers the heuristics are simple: If an object has no preposition in English, it corresponds to accusative in German.

Beyond that, any German learner should buy a German grammar book in their native language that lists the exception, which for an English speaker includes words like "help". (Usually words that admit both interpretations, the help is done to you, but also done for you.)

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Wow, you say "das Keks"? Interesting! I say "der Keks". – Hendrik Vogt Jun 23 '11 at 9:51
@Hendrik Vogt: to avoid discussions I always say "die Kekse" – Takkat♦ Jun 23 '11 at 10:30
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@Gigili: That's true, but the example sentence has the cookie in the Akkusativ, so for a male cookie it would be "einen Keks". – Hendrik Vogt Jun 23 '11 at 10:37
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Das Keks is also correct. I think it's like a lot of other things that are Neutrum in Southern Germany or Austria, like Email or Cola. It is, however, not true that "ein Keks" refers to "das" and "der", because it is accusative in this case, which would be "einen Keks". – OregonGhost Jun 23 '11 at 10:39
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If you think I should change "ein Keks" to "einen Kuss", vote up this comment. – Phira Jun 23 '11 at 11:19
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up vote 6 down vote

The difference lies in the role of the acting parties during the introduction, i.e. who is introduced to whom:

Ich habe ihn einem Freund vorgestellt (Dativ)

The friend receives the main focus, the other person is introduced to the friend.

Ich habe ihm einen Freund vorgestellt (Akkusativ)

The roles switch. The friend is being introduced to the other person.

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