Learn Hardcore Polish: Nasza przewodniczka opowiada nam historię tej góry przy ognisku. - Our guide female tells us the story of this mountain by the campfire.

mówić – “to speak, to say” (general speaking)
powiedzieć – “to say” (single, completed act; perfective)
opowiadać – “to tell, to narrate (a story)” (ongoing or habitual; imperfective)

Here we’re talking about telling a story/history, so opowiadać is the natural choice.

opowiada – present tense, 3rd person singular, imperfective
- can mean “is telling” (right now) or “tells” (regularly), depending on context

If you wanted a completed past action, you’d use the perfective opowiedzieć:

Nasza przewodniczka opowiedziała nam historię tej góry.
“Our guide told us the story of this mountain.” (finished event)

What case is nam and why is it used here?

Nam is the dative plural of the pronoun my (“we/us”).

The verb opowiadać works like English “to tell someone something” and typically takes:

accusative for the thing being told: historię
dative for the person receiving it: nam (“to us”)

So structurally it’s:

opowiada (komu? – to whom?) nam – dative
opowiada (co? – what?) historię – accusative

That’s why the sentence is opowiada nam historię, not opowiada nas historię.

Why is historię ending in -ę instead of just historia?

Historia is a feminine noun. In the sentence it’s the direct object (“(she) tells the story”), so it needs the accusative singular form:

nominative: historia (subject)
accusative: historię (object)

So:

Ta historia jest ciekawa. – “This story is interesting.” (subject, nominative)
Opowiada historię. – “She tells a story.” (object, accusative)

The -ę is the typical ending for many feminine nouns in the accusative singular.

Why do we say tej góry, not ta góra?

Ta góra is nominative (“this mountain” as a subject).
Here, though, góra depends on historia:

historia (czego?) tej góry – “the history/story of this mountain”

In Polish, that “of X” relationship is usually expressed with the genitive case.
So:

nominative: ta góra – “this mountain” (subject form)
genitive: tej góry – “of this mountain”

Some similar patterns:

historia miasta – the history of the city
historia tego miejsca – the history of this place

So tej góry is genitive, required by historia (czego?).

How do I know that tej góry here is genitive and not locative? They look the same.

You’re right that the forms are identical:

tej góry can be genitive or locative feminine singular.

The case is determined by what the governing word requires:

historia (czego?) → genitive → tej góry
o (czym?) – “about (what?)” → locative

Compare:

historia tej góry – the history of this mountain (genitive)
mówi o tej górze – (she) speaks about this mountain (locative)

Here, only historia decides the case, and it wants genitive.

Why is it przy ognisku and not przy ognisko?

The preposition przy (“by, next to, at”) always takes the locative case.

Ognisko (“campfire, bonfire”) is neuter:

nominative: ognisko
locative: ognisku

So with przy you must say:

przy ognisku – by the campfire

Some more examples:

przy stole – by/at the table
przy oknie – by the window
przy rzece – by the river

Never przy + nominative; it’s always przy + locative.

What is the difference between przy ognisku, koło ogniska and obok ogniska?

All can mean physical proximity, but with slight nuances:

przy ognisku – “by/at the campfire”
- often implies being right by it, in its immediate area (e.g., sitting around it)
koło ogniska – “near the campfire”
- neutral “near”, not necessarily as close as “right by”
obok ogniska – “next to the campfire”
- similar to koło, often feels a bit more like “beside”

All three are correct in many contexts; przy ognisku is a very natural choice for “by the campfire” when you’re actually sitting around it.

Why is the word order opowiada nam historię, not opowiada historię nam?

Polish word order is flexible, but there are preferences, especially for short pronouns like nam:

Short pronouns in dative or accusative often appear early in the clause, usually right after the verb or in “second position”.

So:

Nasza przewodniczka opowiada nam historię… – very natural
Nasza przewodniczka opowiada historię nam… – grammatically possible, but sounds marked/odd in neutral speech; it might put unusual emphasis on nam.

You could also say:

Nasza przewodniczka nam opowiada historię tej góry przy ognisku.

The version in your sentence is the most neutral and common.

Can I drop nasza or nam in this sentence?

You can drop nasza if it’s clear from context which guide you mean:
- Przewodniczka opowiada nam historię tej góry przy ognisku.
You usually cannot drop nam, because then you’d lose the information “to us”:
- Przewodniczka opowiada historię tej góry przy ognisku.
  → “The (female) guide tells the story of this mountain by the campfire.”
  (To whom? We don’t know.)

So nasza is more easily omissible, but nam is needed if you want to keep the “to us” meaning.

What tense/aspect is opowiada, and how would I say “was telling us” or “told us”?

Opowiada is:

present tense, imperfective aspect, 3rd person singular

In Polish, aspect and tense interact. For opowiadać / opowiedzieć:

Present, ongoing or habitual:
- (Ona) opowiada nam historię. – She is telling / She tells us the story.
Past, ongoing (“was telling”):
- (Ona) opowiadała nam historię. – She was telling us the story.
Past, completed (“told us”):
- (Ona) opowiedziała nam historię. – She told us the story (finished event).

So you switch to opowiadała (imperfective past) for “was telling” and opowiedziała (perfective past) for “told”.

How do the forms nasza, przewodniczka, historię, tej góry, and ognisku fit together grammatically?

Here is the grammatical “map” of the sentence:

Nasza przewodniczka – subject
- nasza – feminine, singular, nominative (agrees with przewodniczka)
- przewodniczka – feminine, singular, nominative
opowiada – verb (3rd person singular, present, imperfective)
nam – indirect object (dative plural, “to us”)
historię – direct object (feminine, singular, accusative)
tej góry – noun phrase dependent on historię (genitive: “of this mountain”)
- tej – feminine, singular, genitive (agrees with góry)
- góry – feminine, singular, genitive
przy ognisku – adverbial phrase of place
- przy – preposition that requires locative
- ognisku – neuter, singular, locative

Putting it together:
[Subject: Nasza przewodniczka] [Verb: opowiada] [Indirect object: nam] [Direct object: historię (czego?) tej góry] [Place: przy ognisku].