A typical problem when speaking German is to supply a given word the correct article in the relevant context.
As you may know, German is more difficult than English for some reasons:

• Words' genre (there are masculine, feminine and even neutral words)
• Context: Nominative (word is used as a subject), Accusative (word is the direct object of the action), Genitive (word is related to another, e.g. ), Dative (word is the indirect object of the action)

Now, if I say you have to take both of these to supply your listener with some accurate and defekt-frei German sentences, you might want to learn something else instead.
Happily, some colleague just gave me his solution to this puzzle:
It comes as a matrix:

R    E    S    E
N    E    S    E
M    R    M    N
S    R    S    R

The columns respectively stand for Masc, Fem. Neut. and Plural.
The lines stand for Nominative, Accusative, Dative and Genitive.
The letter displayed at each position stand for the last letter of the article to be used.
Except with DAS which becomes DES in non-nominative contexts, R, E, M and N, respectively stand for DER, DIE, DEM and DEN.

Now, let's make some tries:

• Ich kusse das Kind. (acc/neutral) (I kiss the child)
• Der Regenschirm der Dame (nom/masc. and fem./gen.) (The woman's umbrella)
• Aus dem Haus (neutr.dat.) (out of the house)

(Of course, my German friends can still come to me and correct my awfully-sounding mistakes so that it will also be a relevant exercise for them... ;-)