På onsdag skal vi til at betale, så jeg finder mit kort frem med det samme.

It means on Wednesday, and in many contexts it is understood as this coming Wednesday.

A few useful points:

• på is the normal preposition with days in expressions like på mandag, på tirsdag, på onsdag
• Danish often relies on context to show which Wednesday is meant
• If you want to talk about last Wednesday, Danish typically says i onsdags

So på onsdag is a very normal way to say on Wednesday / this Wednesday.

In Danish, days of the week and months are normally written with a lowercase letter.

So:

• onsdag = Wednesday
• januar = January

This is different from English, where both are capitalized.

Because Danish follows the V2 rule in main clauses. That means the finite verb usually comes in the second position.

Here, På onsdag has been placed first, so the verb skal must come next:

• På onsdag skal vi til at betale

Structure:

• 1st position: På onsdag
• 2nd position: skal
• then subject: vi

If there were no fronted time expression, you would say:

• Vi skal til at betale på onsdag

Skal often suggests something that is:

• planned
• expected
• necessary
• part of an arrangement or obligation

So skal vi til at betale sounds like we’re going to have to start paying or we’re due to start paying.

By contrast, vil is more neutral for future meaning, and it can also mean want to depending on context.

Compare:

• Vi skal betale = we have to / we are supposed to pay
• Vi vil betale = we will pay, or we want to pay, depending on context

So skal is a natural choice here.

Til at + infinitive adds the idea of starting or being about to begin an action.

So:

• Vi skal betale = we have to pay
• Vi skal til at betale = we have to start paying / we’re about to start paying

In this sentence, til at makes the action feel like the next step that is coming up. It highlights the onset of paying, not just the fact of paying in general.

Yes. Danish can leave the object unstated if it is obvious from context.

So betale by itself can mean things like:

• pay
• pay up
• make the payment

The sentence does not say exactly what is being paid, because that is apparently already understood.

If needed, Danish could add an object, for example:

• betale regningen = pay the bill
• betale for det = pay for it

Because så jeg finder mit kort frem med det samme is a new clause.

Danish comma rules often place a comma between clauses, especially when both clauses have their own finite verb:

• skal in the first clause
• finder in the second clause

So the comma helps mark the clause boundary:

• På onsdag skal vi til at betale, så jeg finder mit kort frem med det samme.

Here så means so, and it works as a conjunction joining two clauses.

After a conjunction like this, the normal main-clause order is used:

• så jeg finder ...

That is different from sentence-initial så meaning then/so, where så takes the first position and the verb comes second:

• Så finder jeg mit kort frem med det samme.

So both are possible, but they are structured differently:

• ..., så jeg finder ... = ..., so I get/take out ...
• Så finder jeg ... = Then/so I get/take out ...

Because Danish often uses the present tense for future meaning when the context already makes the time clear.

Here the future time is established by:

• På onsdag
• skal

So jeg finder can naturally refer to what happens then.

This is very common in Danish. English sometimes does something similar, but Danish uses it even more freely.

Finde ... frem is a very common Danish verb-particle combination.

In this sentence, it means something like:

• take out
• get out
• produce
• fetch

So jeg finder mit kort frem means I get my card out or I take out my card.

Why is frem separated?

Because in Danish, particles like frem are often placed later in the clause when the verb is finite:

• Jeg finder mit kort frem

You can think of it as similar to English phrasal verbs:

• take out the card
• get the card out

Because kort is a neuter noun in Danish.

The possessive forms are:

• min for common-gender singular nouns
• mit for neuter singular nouns
• mine for plural nouns

Since it is:

• et kort = a card

the correct possessive is:

• mit kort = my card

Compare:

• en bil → min bil
• et kort → mit kort
• bøger → mine bøger

It is a fixed expression meaning:

• immediately
• right away
• straight away

So:

• jeg finder mit kort frem med det samme
  means
• I get my card out immediately

Even though the words literally look like with the same, you should learn med det samme as a set phrase meaning at once / immediately.