Jeg lægger frugt og grøntsager i indkøbsvognen, før jeg går til kassen.

Because lægger and går are the present-tense forms used in a full sentence.

• at lægge = to put / to lay

• jeg lægger = I put / I am putting

• at gå = to go / to walk
• jeg går = I go / I am going

Danish often uses the present tense for something happening now, something habitual, or something that happens next in a sequence. After før, Danish also uses the present tense naturally: før jeg går = before I go.

This is a very common Danish distinction:

• lægge = to put / lay something somewhere (action)
• ligge = to lie / be lying somewhere (state)

So in this sentence, jeg lægger frugt og grøntsager i indkøbsvognen means the speaker is actively placing the items in the cart.

After that, you could say:

Frugten ligger i indkøbsvognen = the fruit is lying in the shopping cart.

Because Danish does not use an article here.

• frugt is being used as a general or uncountable noun, like English fruit
• grøntsager is an indefinite plural, and Danish has no plural form of a/an

So:

• frugt = fruit
• grøntsager = vegetables

This is very natural when talking about items in general, not specific ones.

Because Danish often treats frugt like a mass noun, similar to English fruit.

So:

• frugt = fruit in general
• grøntsager = vegetables in general

You can sometimes see frugter, but frugt og grøntsager is a very common and natural pairing.

Because Danish usually adds the definite article to the end of the noun.

• en indkøbsvogn = a shopping cart
• indkøbsvognen = the shopping cart

The same thing happens with kassen:

• en kasse = a box / a checkout
• kassen = the box / the checkout

So instead of a separate word like English the, Danish often attaches it to the noun.

Yes. Danish loves compound nouns.

indkøbsvogn is made from:

• indkøb = shopping
• vogn = cart / trolley

Together, they form one word: indkøbsvogn = shopping cart / shopping trolley.

This is completely normal in Danish. English often writes similar ideas as two words, but Danish usually joins them.

Because the prepositions express different ideas:

• i = in / inside
• til = to / toward

So:

• lægger ... i indkøbsvognen = put ... in the shopping cart
• går til kassen = go to the checkout

You are putting the items inside the cart, but moving toward the checkout.

In a shop, kassen usually means the checkout, the register, or the till.

So here it does not mean just any box. It is store vocabulary.

That is why gå til kassen means go to the checkout.

If you were already there, you might say:

Jeg står ved kassen = I am standing at the checkout.

Because før jeg går til kassen is a subordinate clause.

In Danish, many writers place a comma before a subordinate clause like this. So the comma is normal.

You may also see sentences without that comma, depending on comma style and personal or editorial preference. But the version with the comma is absolutely standard and very common.

Because after a subordinating word like før, Danish uses subordinate-clause word order.

In a main clause, Danish often puts the verb early:

• Jeg går til kassen

But in a subordinate clause, the subject normally comes before the verb:

• før jeg går til kassen

So før går jeg would sound wrong here.

Yes, often you can.

Jeg lægger frugt og grøntsager i indkøbsvognen, inden jeg går til kassen is also possible.

In this sentence, før is very natural and common. Inden can sound a little more formal or a little more explicit in some contexts, but both can mean before.

Yes, in everyday Danish you often could.

• jeg lægger ... i indkøbsvognen
• jeg putter ... i indkøbsvognen

Both are natural. Putter often emphasizes putting something into a container or space. Lægger is also very normal here and may sound slightly more neutral.

So the original sentence is good Danish, and putter would be a possible alternative, not a correction.