When speaking German, when do you use "der" and when do you use "den"?

Answer 1

der is nominative and den accusative:

Nominative (Wer?): The subject of a sentence, the thing doing the action

Accusative (Wen?): The direct object, the thing which is directly receiving the action, or the object of certain prepositions

http://en.wikipedia.org/wiki/German_grammar

Answer 2

There are two main times you do that:

(1.) If you have a masculine noun like Mann, you say der Mann when the man is doing the action and den Mann when the man is receiving the action.
Der Mann küsst die Frau. He kisses her.
Die Frau küsst den Mann. She kisses him.

(2.) You also say den instead of der if the masculine word comes after certain prepositions like
durch (through): durch den Tunnel
für (for): für den Mann
gegen (against): gegen den Mann
ohne (without): ohne den Hund
um (around, like around the perimeter of): um den Park
- - - - - -
There are some other things, too, but I don't want to be really confusing. Ask again if you want the whole story and I'll tell you about dative case and accusative of time and two-way prepositions, ... I didn't *think* you wanted to know all that right now!

Answer 3

You are presumably speaking of masculine nouns only (I ask because both der and den have other uses, which we can discuss separately). For masculine nouns in the singular, der is the subject (nominative), while den is the direct object (accusative). So we say Der Mann sah den Knaben 'The man saw the boy', Der Knabe schlug den Hund 'The boy hit the dog', Der Deutsche trank den Wein 'The German man drank the wine'. The order of the words does not matter. We can also say Den Knaben sah der Mann and it still means 'The man saw the boy', and so on. If this is not clear or you need more info, please ask. As I say there are other uses of der and den in the feminine or the plural that I am going into here.