Jeg er nødt til at bestille tid hos tandlægen, fordi min tand gør ondt.

Er nødt til at means have to, need to, or more literally be forced/obliged to do something.

So:

• Jeg er nødt til at bestille tid = I have to book an appointment

A few useful notes:

• nødt is used with være:
  
  • jeg er nødt til at ...
  • du er nødt til at ...
  • vi er nødt til at ...
• It often sounds a bit stronger than just I should. It suggests necessity.

Compared with other Danish expressions:

• jeg skal ... = I have to / I’m supposed to ...
• jeg må ... = I must / am allowed to ... depending on context
• jeg er nødt til at ... = I really need to / have no choice but to ...

So in this sentence, the speaker is saying it is necessary to make the appointment.

This is just the normal structure of the expression være nødt til at + infinitive.

Pattern:

• jeg er nødt til at gå = I have to go
• hun er nødt til at arbejde = she has to work
• vi er nødt til at vente = we have to wait

So:

• nødt til = obliged/forced/required to
• at bestille = to book

You should learn er nødt til at as one chunk, because Danish uses this pattern very regularly.

Bestille tid is a very common Danish expression meaning book an appointment or make an appointment.

Literally:

• bestille = order/book/reserve
• tid = time

So the idea is to book a time.

This is very natural Danish when talking about doctors, dentists, hairdressers, and similar services.

Examples:

• Jeg skal bestille tid hos lægen. = I need to book an appointment with the doctor.
• Har du bestilt tid? = Have you made an appointment?

English uses make an appointment, but Danish often uses bestille tid instead.

In Danish, hos is commonly used when you mean with / at the place of a professional person, especially someone you go to for treatment or service.

So:

• hos tandlægen = at/with the dentist
• hos lægen = at/with the doctor
• hos frisøren = at the hairdresser’s

This is a very common usage.

If you said til tandlægen, it would more strongly suggest movement to the dentist, like physically going there. But in the context of bestille tid, Danish normally says:

• bestille tid hos tandlægen

because the appointment is with that professional.

Tandlægen is the definite form: the dentist.

• en tandlæge = a dentist
• tandlægen = the dentist

In Danish, people often use the definite form when talking about familiar institutions or professionals that fit the situation naturally, especially health services.

So:

• hos tandlægen sounds like at the dentist
• not necessarily one specific named dentist in the conversation, but the dentist as the relevant professional

This is similar to how English often says:

• I need to go to the dentist
• not I need to go to a dentist, unless you want to emphasize that it could be any dentist

Fordi means because.

It introduces the reason:

• Jeg er nødt til at bestille tid hos tandlægen = I have to book an appointment with the dentist
• fordi min tand gør ondt = because my tooth hurts

So the whole sentence has:

1. the main statement
2. the explanation for it

Very common examples:

• Jeg bliver hjemme, fordi jeg er træt. = I’m staying home because I’m tired.
• Hun går tidligt, fordi hun skal arbejde. = She is leaving early because she has to work.

Because after fordi, Danish normally keeps subject + verb order in ordinary statements.

So:

• min tand = subject
• gør = verb

That gives:

• fordi min tand gør ondt

This is different from Danish main clauses, where the verb is often in second position.

Compare:

• Main clause: I dag går jeg til lægen.
• Subordinate clause: ... fordi jeg går til lægen i dag.

After fordi, you normally do not invert the subject and verb.

Gør ondt literally means does hurt or makes pain, but in natural English it simply means:

• hurts
• is painful

So:

• Min tand gør ondt. = My tooth hurts.
• Det gør ondt. = It hurts.

This is a very common Danish expression for pain.

Examples:

• Mit hoved gør ondt. = My head hurts.
• Min ryg gør ondt. = My back hurts.
• Gør det ondt? = Does it hurt?

It is worth learning as a fixed phrase: gøre ondt = to hurt / to be painful.

Because in Danish, possessives like min, din, hans, hendes, vores already make the noun definite in meaning.

So you say:

• min tand = my tooth
• din bil = your car
• vores hus = our house

You do not add the definite ending as well.

So these are correct:

• min tand
• min bil
• mit hoved

And these are wrong:

• min tanden
• min bilen

This is similar to English: you say my tooth, not my the tooth.

Because the speaker is talking about one specific tooth that hurts:

• min tand gør ondt = my tooth hurts

If more than one tooth hurt, you could say:

• mine tænder gør ondt = my teeth hurt

So the singular/plural choice depends on the situation:

• tand = tooth
• tænder = teeth

Yes, you could say:

• Jeg skal bestille tid hos tandlægen...

That would also be natural, but it is slightly different in tone.

• Jeg er nødt til at ... emphasizes necessity: I have to / I really need to
• Jeg skal ... can mean I have to, I’m going to, or I’m supposed to, depending on context

So in this sentence:

• Jeg er nødt til at bestille tid hos tandlægen sounds a bit stronger and more urgent
• Jeg skal bestille tid hos tandlægen is also fine, but slightly less forceful

Because the tooth hurts, er nødt til at fits very well.

A rough pronunciation guide might be:

• Jeg er nødt til at bestille tid hos tandlægen, fordi min tand gør ondt.

Approximate English-friendly version:

• yai air NERTH til ah be-STEE-lee teeð hos TAN-lay-en, for-DEE min tan GUR ond

A few important pronunciation points:

• jeg is often pronounced something like yai or yigh, depending on the speaker
• nødt has a vowel that does not exist in English; you have to learn it by listening
• tandlægen often sounds more compressed in real speech than the spelling suggests
• gør also has a Danish vowel that English does not really have
• ondt ends with a soft t sound or may sound reduced in fast speech

The best approach is to listen to native audio and repeat the whole sentence as a chunk rather than trying to pronounce each word separately.

Yes, very natural.

A Danish speaker would absolutely say:

• Jeg er nødt til at bestille tid hos tandlægen, fordi min tand gør ondt.

It sounds like normal spoken or written Danish.

You could also hear close variants like:

• Jeg må hellere bestille en tid hos tandlægen, fordi jeg har tandpine.
  = I’d better book an appointment with the dentist because I have toothache.
• Jeg skal til tandlægen, fordi jeg har ondt i en tand.
  = I’m going to the dentist because I have pain in a tooth.

But your original sentence is completely idiomatic and natural.

A learner would benefit from memorizing these as chunks:

• jeg er nødt til at ... = I have to / I need to ...
• bestille tid = book an appointment
• hos tandlægen = at/with the dentist
• fordi = because
• gør ondt = hurts

If you learn them as fixed expressions, you will be able to build many similar sentences:

• Jeg er nødt til at ringe til lægen.
• Jeg skal bestille tid hos frisøren.
• Mit knæ gør ondt.
• Jeg bliver hjemme, fordi jeg er syg.

This is often more useful than memorizing each word completely on its own.