I'm not a native speaker but the common way to use the definite article is via suffix. So you add -[i]nn (male) -[i]n (female) -[i]ð (neuter) to the noun, these are the paradigms in the nominative case. But you can place it on the beginning as well. However "Hins" will be used in genitive case, so you rather use "Hinn".

Lífthrasir is correct but I want to add: Hins rauða hundur and Rauða hundurinn are not correct gramatically nominative: hinn rauði hundur accusative: hinn rauða hund dative: hinum rauða hundi genitive: hins rauða hunds nominative: rauði hundurinn accusative: rauða hundinn dative: rauða hundinum genitive: rauða hundsins