I dag lærer vi at bruge “om ... eller ...” og “om ... så ...”, når resultatet er det samme.

Because Danish main clauses usually follow the V2 rule: the finite verb comes in the second position.

• Vi lærer i dag ... = neutral order
• I dag lærer vi ... = the time phrase I dag is moved to the front, so the verb lærer must come right after it

That is why vi comes after lærer here.

Lærer is the present tense of at lære.

In a sentence like this, Danish present tense can often match English:

• Today we learn ...
• Today we are learning ...
• sometimes even Today we’ll learn ... in a teaching context

So the present tense is completely natural here.

Because at bruge is an infinitive, and lære at + infinitive means learn to + verb.

So:

• lære = learn
• at bruge = to use
• lære at bruge = learn to use

Compare:

• Vi lærer dansk. = We learn Danish.
• Vi lærer at bruge denne struktur. = We learn to use this structure.

Here, om means whether or sometimes if, not about.

Danish om can have several meanings depending on context, for example:

• en bog om Danmark = a book about Denmark
• om vinteren = in winter
• jeg ved ikke, om han kommer = I don’t know whether he is coming

In your sentence, it is the whether/if meaning.

Om ... eller ... is used to present alternatives, much like English whether ... or ....

It is used when the main result does not change, no matter which option is true.

Example:

• Om det regner eller sner, går vi ud. = Whether it rains or snows, we go out.

So this pattern explicitly names two possibilities.

In this kind of use, om ... så ... often has the sense of even if ... or whether ... then still .... It usually emphasizes that the result stays the same anyway.

A simple way to see the difference:

• om ... eller ... = names two alternatives
• om ... så ... = mentions one condition, but the result still holds

Example:

• Om det så regner, går vi ud alligevel. = Even if it rains, we are going out anyway.

So så often adds an emphatic still / anyway / even then feeling.

Because når is often used for a general situation or a rule-like statement: when the result is the same.

Here the sentence is explaining a grammar rule, so når fits well:

• når resultatet er det samme = when the result is the same

If you used hvis, it would sound more like a specific hypothetical case:

• hvis resultatet er det samme = if the result is the same

Both can be understandable in some contexts, but når is more natural here because this is a general explanation.

Resultatet is the definite form of et resultat.

• et resultat = a result
• resultatet = the result

Here Danish uses the definite form because it refers to the outcome in that situation in a general, identifiable way. English often does something similar: when the result is the same.

Det samme means the same.

So:

• resultatet er det samme = the result is the same

This is a very common Danish expression. You will also see it in sentences like:

• Vi gjorde det samme som i går. = We did the same as yesterday.
• Det er det samme for mig. = It’s the same to me / It doesn’t matter to me.

That comma marks the start of a subordinate clause: når resultatet er det samme.

In Danish, you may see two punctuation styles:

• with a start comma
• without a start comma

So both of these can occur:

• ..., når resultatet er det samme
• ... når resultatet er det samme

The version in your sentence is perfectly normal.

Because the sentence is talking about the expressions themselves, not using them normally inside the sentence.

In English, we often do the same when discussing words or grammar patterns.

So the quotation marks are just there to show:

• these are the forms being taught
• they are examples of language, not ordinary content words in the sentence

In running Danish sentences, you would normally not put quotation marks around them unless you were discussing the expressions themselves.

Yes:

With om ... eller ...

• Om du tager bussen eller toget, kommer du frem. = Whether you take the bus or the train, you get there.
• Om han er hjemme eller på arbejde, kan vi ringe til ham. = Whether he is at home or at work, we can call him.

With om ... så ...

• Om det så er dyrt, køber jeg det. = Even if it is expensive, I’ll buy it.
• Om du så er træt, må du komme alligevel. = Even if you are tired, you still have to come.

These show the main idea: the outcome stays the same.