Jeg siger tak, når tjeneren kommer med vores bestilling.

Both are possible, but sige tak is a very common everyday way to express to say thank you in Danish.

• Jeg siger tak = I say thanks / I say thank you
• Jeg takker = I thank

Jeg takker can sound a bit more formal, deliberate, or stylistically marked in some contexts. Jeg siger tak is often the more natural conversational choice.

Here når means when.

It is used for:

• something that happens generally or repeatedly
• something expected to happen in the future

So this sentence can mean something like a general habit or a future situation.

Compare:

• når = when
• da = when, but usually about one specific event in the past
• hvis = if

Examples:

• Når tjeneren kommer, siger jeg tak. = When the waiter comes, I say thank you.
• Da tjeneren kom, sagde jeg tak. = When the waiter came, I said thank you.
• Hvis tjeneren kommer, siger jeg tak. = If the waiter comes, I say thank you.

Because tjeneren is the definite form: the waiter.

In Danish, definiteness is often shown by adding an ending to the noun:

• en tjener = a waiter
• tjeneren = the waiter

So instead of using a separate word for the, Danish often attaches it to the noun.

Literally, kommer med means comes with, but in many situations it is naturally used for bringing something.

So:

• tjeneren kommer med vores bestilling = the waiter brings our order

This is very natural Danish. You could also say bringer, but kommer med is common and idiomatic in speech.

Compare:

• Tjeneren kommer med maden. = The waiter brings the food.
• Tjeneren bringer maden. = The waiter brings the food.

Both work, but kommer med often sounds more everyday and conversational.

Because possessives like min, din, vores, and deres normally replace the article.

So:

• vores bestilling = our order

Not:

• den vores bestilling

This is similar to English, where you say our order, not the our order.

In modern Danish, vores is the normal everyday word for our.

• vores = the usual modern form
• vor, vort, vore = more formal, literary, old-fashioned, or used in fixed expressions

So vores bestilling is the normal choice in ordinary speech and writing.

Because that is the present tense in Danish.

Danish verbs do not change for person the way English verbs sometimes do. The same present-tense form is used with all subjects.

For example:

• jeg siger
• du siger
• han siger
• vi siger

And:

• jeg kommer
• du kommer
• de kommer

So siger and kommer are just the normal present-tense forms.

After når, you have a subordinate clause, and the word order is different from main-clause word order.

In the sentence:

• når tjeneren kommer med vores bestilling

the order is:

• når
  • subject + verb

That is normal for a subordinate clause in Danish.

If you put the når clause first, the main clause changes word order because Danish main clauses follow the verb-second rule:

• Når tjeneren kommer med vores bestilling, siger jeg tak.

Notice that it becomes siger jeg, not jeg siger.

Because når tjeneren kommer med vores bestilling is a subordinate clause.

Many Danish writers put a comma before a subordinate clause like this:

• Jeg siger tak, når tjeneren kommer med vores bestilling.

You may also sometimes see it without that comma, depending on comma style:

• Jeg siger tak når tjeneren kommer med vores bestilling.

So the comma is very normal here, but Danish comma practice can vary.

Yes. Bestilling is a very natural word for order in this context.

It can mean:

• an order
• a booking
• something that has been requested

In a restaurant, vores bestilling means the food or drinks we ordered.

A word like ordre also exists in Danish, but in restaurant situations bestilling is usually the more natural choice.