Learn Russian: Мы готовим горячую еду бездомным людям.

In Russian, the Dative case is used for the recipient of an action (the indirect object). Since we are cooking food for the homeless people, they go in the Dative case. Notice how Russian doesn't need a preposition like 'for' here; the case ending does that job for us.

How do the Dative plural endings work for бездомным людям?

For plural nouns in the Dative case, the endings are usually -ам or -ям. The noun люди (people) takes the soft ending, becoming людям. For plural adjectives, the endings are -ым or -им. The adjective бездомные (homeless) takes the hard ending, becoming бездомным.

Why are we using горячую еду instead of the dictionary forms?

Because the hot food is the direct object being cooked, it needs to be in the Accusative case. The noun еда (food) is feminine, so its -а ending changes to -у (еду). The matching feminine adjective горячая (hot) changes its -ая ending to -ую (горячую).

What is the singular form of людям?

This is a highly irregular word! The Nominative singular is человек (person). But in the plural, the word changes completely to люди (people). людям is the Dative plural form of люди.