Learn Icelandic: Lykillinn er í skúffu.

The preposition í (in) requires the following noun to be in the dative case when describing a stationary location. For feminine nouns ending in -a like skúffa, the dative form changes the -a to a -u.

How do we know it means 'in a drawer' and not 'in the drawer'?

Icelandic does not use a separate word for 'a' or 'an'. A plain, bare noun like skúffu simply means 'a drawer'. If we wanted to say 'in the drawer', we would add the definite article to the end of the word, making it í skúffunni.

What does the -inn at the end of lykillinn do?

That is the Icelandic way of saying 'the'. The basic dictionary word for 'key' is lykill. Since it is a masculine word, adding the definite article ('the') to the end turns it into lykillinn.

Does í always force the noun into the dative case like it does here?

Not always! Prepositions like í and á take the dative case for a static location (where something rests, like this key). But if a sentence describes movement into a place (like putting a key into a drawer), these same prepositions take the accusative case instead.