Learn Russian: Когда мы пришли домой, папа уже спал. - When we came home, dad was already asleep.

This sentence perfectly shows how Russian uses verb aspects. пришли (arrived/came) is perfective because it represents a completed, one-time event. спал (was sleeping) is imperfective because it describes an ongoing action happening in the background when that completed event took place.

Why is the word for home домой instead of дома?

Russian uses different words for location and direction. дома means being located "at home". But because the verb пришли involves motion towards a destination, you must use the directional word домой (homewards / to home).

The word папа ends in "-a", which usually marks a feminine noun. Why is the verb спал masculine?

While most nouns ending in "-a" are feminine, words that refer specifically to male people are masculine, regardless of their ending. Because папа (dad) is biologically male, it requires the masculine past tense verb спал rather than the feminine спала.

What is the dictionary form of пришли? It doesn't look like a standard past tense verb.

The dictionary form (infinitive) is прийти (to arrive on foot). It is a verb of motion, and its past tense forms are highly irregular. Instead of just dropping the ending, it changes to пришёл for masculine, пришла for feminine, and пришли for plural (like мы).