Learn Hardcore Russian: Карта лежит на столе.

Because it’s the subject of the sentence. In Russian, the noun that performs the action or “is” in a state of being is in the nominative case. Here карта (map) is singular and feminine, so it appears as карта.

What does the verb лежит mean, and why is it used here instead of something like “is lying”?

Лежать means “to lie” (in the sense of “to be in a horizontal position”). Лежит is the 3rd person singular present tense of the imperfective verb лежать. It translates naturally into English as “lies” or “is lying.” Russian does not need a separate auxiliary verb “is” plus a participle; the single word лежит covers both.

Why is столе in the prepositional case?

When you talk about location “on” something with the preposition на, and you mean a static location (not movement toward or away), the noun that follows is put into the prepositional case. Here you’re describing where the map is located, so стол (table) becomes столе.

Could you use a different preposition instead of на?

You could say в + prepositional only if the object is inside something (e.g. в комнате “in the room”). A map can’t be “in the table,” so в столе wouldn’t make sense. For “on the table,” на is correct.

Why don’t we need an article like “the” or “a” in Russian?

Russian has no articles. Context or word order often tells you whether you mean “a map,” “the map,” or “this map.” If you really need to specify, you can add words like эта (this) or какая-то (some), but there is no direct equivalent of “the” or “a.”

How do you pronounce столе, and where is the stress?

You pronounce it as [sta-LYE]. The stress is on the second syllable: сто-ЛЕ.

Can I change the word order, for example, say На столе лежит карта instead of Карта лежит на столе?

Yes. Russian word order is relatively flexible.

Карта лежит на столе (neutral S-V-Adverbial)
На столе лежит карта (emphasizes location)
Both mean “The map is lying on the table,” but the second puts more focus on where the map is.