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