Learn Hardcore Danish: Jeg køber sko på udsalget i byen. - I buy shoes at the sale in the city.

Context decides which is meant.
So Jeg køber sko på udsalget i byen can mean either I buy shoes at the sale in town or I’m buying shoes at the sale in town, depending on situation.

Why is sko used for shoes – where is the plural ending?

Sko is one of those Danish nouns where the singular and plural have the same form:

en sko = a shoe
sko = shoes (indefinite plural)
skoene = the shoes (definite plural)

So in Jeg køber sko, the word sko is plural because of the context and the verb meaning. If you wanted just one shoe, you’d say Jeg køber en sko.

Why is it på udsalget and not i udsalget or ved udsalget?

Danish prepositions are often idiomatic, and they don’t always match English:

på udsalget literally: on the sale, but it means at the sale (a sale event)
i is typically used for being inside something (a room, a box, a building)
ved is more like by / next to / near

For organized activities, events, institutions etc., Danish often uses på:

på arbejde = at work
på universitetet = at the university
på museum = at the museum
på udsalget = at the sale

So på udsalget is the natural choice when you mean “at the sale (event).”

Why is it udsalget and not just udsalg? What does the -et mean?

Udsalg is a neuter noun:

et udsalg = a sale
udsalget = the sale

Danish usually marks “the” by adding an ending to the noun instead of using a separate word:

en by = a town
byen = the town
et udsalg = a sale
udsalget = the sale

So på udsalget literally is on the sale, i.e. at the sale. The -et is the definite article (the) for neuter nouns.

What is the gender of udsalg, and why does that matter?

Udsalg is neuter (in Danish: intetkøn). That matters because:

The indefinite article is et: et udsalg
The definite ending is -et: udsalget

For common gender (en-words) you would have en and -en instead, e.g.:

en by (a town) → byen (the town)

So in this sentence we see both genders:

udsalg → udsalget (neuter)
by → byen (common gender)

Why is it i byen and not på byen?

For locations like towns and cities, Danish uses i:

i byen = in the town
i København = in Copenhagen
i London = in London

På is used with certain types of places (islands, some institutions, events, etc.), but byen here is treated as a normal town, so you use i byen.

Thus på udsalget i byen is literally at the sale in the town.

Why does byen mean the town? Where is the word the?

Danish usually does not use a separate word for the. Instead, it attaches an ending to the noun:

en by = a town
byen = the town

Pattern for this common-gender noun:

en by = a town (indefinite singular)
byen = the town (definite singular)
byer = towns (indefinite plural)
byerne = the towns (definite plural)

So i byen literally is in the town.

Is the word order Jeg køber sko på udsalget i byen fixed, or can I move things around?

The basic order here is:

Subject – Verb – Object – Place
Jeg – køber – sko – på udsalget i byen

This is a very natural, neutral order. You can move elements for emphasis, because Danish is a V2 language (the finite verb must be in second position in main clauses):

I byen køber jeg sko på udsalget.
(In town, I buy / I’m buying shoes at the sale.)

Notice that when you move something to the front, køber stays in second position. However, the original sentence Jeg køber sko på udsalget i byen is the most typical, unmarked version.

Could the sentence also refer to the future, like I’m going to buy shoes…?

Yes. Danish often uses the present tense to talk about the near future, especially when it’s a plan or arrangement:

Jeg køber sko på udsalget i byen (i morgen).
= I’m going to buy shoes at the sale in town (tomorrow).

If you want to emphasise the future even more, you can also say:

Jeg skal købe sko på udsalget i byen.
(I’m supposed to / I will / I’m going to buy shoes at the sale in town.)

But Jeg køber… with a future time expression is very normal.

Is køber here only a verb, or can it also be a noun?

In this sentence, køber is a verb (present tense of at købe = to buy):

jeg køber = I buy / I’m buying

But køber can also be a noun meaning buyer:

en køber = a buyer
køberen = the buyer

You tell them apart by position in the sentence and context. After a subject like jeg, du, han, it will usually be the verb: jeg køber, du køber, etc.

How do you pronounce the words køber, sko, udsalget, and byen?

Approximate English-like hints (not exact IPA):

køber: the ø is like the vowel in British “bird” or French “deux”, but with rounded lips. The r is soft and can influence the vowel; in many accents it sounds a bit like “KØ-bå”.
sko: close to “sko” in “skool” without the l, or English “sko”; a long o sound.
udsalget: roughly “OOL-sal-yeth”, but shorter and more clipped; d in ud is very soft or almost gone in normal speech, and -get is pronounced together as one beat.
byen: “BUU-en” but with a rounded y sound (like French u in “tu”); not like English “bye-en”.

Precise pronunciation varies slightly by region, but these approximations help you get close.