Kończy się papier w drukarce, więc muszę iść do sklepu.

Kończyć się is the intransitive/reflexive-style form of kończyć.

• kończyć = to finish something
• kończyć się = to come to an end, to run out

So in this sentence, Kończy się papier means The paper is running out.

The się is important because without it, kończyć would usually need an object, as in Kończę pracę = I am finishing the work. With się, the idea becomes something is ending / running out on its own.

Because kończy się describes an ongoing process: the paper is not necessarily completely gone yet, but it is running out.

Compare:

• Kończy się papier = The paper is running out
• Skończył się papier = The paper has run out / The paper is gone

The first sounds like a developing situation. The second sounds completed. In everyday speech, kończy się is very natural when you notice supplies are getting low.

Because papier is the grammatical subject of kończy się.

In Kończy się papier, the thing that is running out is papier, so it stays in the nominative singular form.

A native English speaker may expect something more like I am running out of paper, but Polish often structures this as Paper is running out. That is why papier is the subject here.

Because the preposition w means in here, and when it refers to location, it normally takes the locative case.

So:

• drukarka = printer
• w drukarce = in the printer

This is a very common pattern:

• w domu = in the house / at home
• w szkole = at school
• w samochodzie = in the car

So papier w drukarce means paper in the printer.

Because Polish does not have articles like a or the.

So papier can mean:

• paper
• the paper
• sometimes some paper

And do sklepu can mean:

• to a shop
• to the shop

The exact meaning comes from context. In this sentence, English naturally uses the paper and the store/a store, but Polish does not need separate words for that.

Więc means so, therefore, or thus.

It connects the two parts of the sentence:

• Kończy się papier w drukarce = the paper in the printer is running out
• więc muszę iść do sklepu = so I have to go to the store

The comma before więc is standard in Polish when it joins clauses like this. It works much like English punctuation before so in a sentence of this type.

Both can be possible, but they are not exactly the same.

• muszę iść = I have to go
• muszę pójść = I have to go / I need to go, with a stronger sense of a single completed trip

After modal verbs like musieć, Polish often uses the imperfective infinitive, especially when talking about necessity in a general or immediate sense. So muszę iść do sklepu is very natural.

Using muszę pójść do sklepu is also possible, but it can sound a bit more like I need to make that trip or I have to go there once.

Because Polish usually drops subject pronouns when the verb ending already shows who the subject is.

• muszę clearly means I must / I have to
• the ending -ę tells you it is first person singular

So ja is unnecessary unless you want emphasis or contrast:

• Muszę iść do sklepu. = I have to go to the store.
• Ja muszę iść do sklepu, nie ty. = I have to go to the store, not you.

This is one of the big differences from English, where the subject usually must be stated.

Because the preposition do requires the genitive case.

So:

• sklep = shop, store
• do sklepu = to the shop / to the store

This is a very important pattern in Polish:

• do domu = to home / home
• do szkoły = to school
• do pracy = to work

So whenever you use do, you normally need the genitive form of the noun.

Yes. Polish word order is more flexible than English word order.

The original sentence is natural and clear:

Kończy się papier w drukarce, więc muszę iść do sklepu.

But other orders are possible, for example:

• Papier w drukarce się kończy, więc muszę iść do sklepu.
• Muszę iść do sklepu, bo kończy się papier w drukarce.

The meaning stays similar, but the focus can shift slightly. The original version sounds neutral and idiomatic.

No. There are several natural ways to express the same basic idea.

For example:

• Kończy się papier w drukarce. = The paper in the printer is running out.
• Skończył się papier w drukarce. = The paper in the printer has run out.
• Kończy mi się papier w drukarce. = I’m running out of paper in the printer.

That last version, with mi, is especially common in everyday Polish because it adds the idea that this is happening to me / for me. It often sounds very natural when talking about your own supplies or belongings.