First Things First - we have to know what articles do we have:
Maskulinum (he) - Femininum (she) - Neutrum (it)
and also Plural.
They look so in our four cases:
Nominativ: der, die, das, die 
Genitiv: des, der, des, der 
Dativ: dem, der, dem, den 
Akkusativ: den, die, das, die 
To answer your question you need to learn what case do you use after prepositions. 
aus - Dativ 
mit - Dativ 
nach - Dativ 
von - Dativ 
zu - Dativ 
So:
1. FEMINE article change to DER 
2. NEUTER article change to DEM 
3. MASCULINE article change to DEM