Tandlægen lægger lokalbedøvelse, før hun borer i tanden.

Tandlægen is made from:

• tand = tooth
• læge = doctor

So tandlæge literally means tooth doctor, i.e. dentist.

The ending -en is the usual definite ending for many common-gender nouns, so:

• en tandlæge = a dentist
• tandlægen = the dentist

Danish usually puts the definite article at the end of the noun instead of using a separate word like English the.

Because Danish, like German, very often forms compound nouns as a single word.

Here:

• lokal = local
• bedøvelse = anesthesia / numbing

So lokalbedøvelse = local anesthesia.

In Danish, writing this as one word is normal and expected.

Here lokalbedøvelse is being used like an uncountable medical substance or procedure, much like English local anesthesia.

So:

• lægger lokalbedøvelse = applies/administers local anesthesia

If you added en, it would sound more like a local anesthetic / an anesthetic injection as a single countable item.

Literally, lægge often means lay, put, or place. But in medical contexts it can also mean apply or administer.

So in this sentence:

• Tandlægen lægger lokalbedøvelse = The dentist administers local anesthesia

This is a good example of a verb not translating word-for-word even if its basic meaning is more concrete.

Both are in the present tense:

• lægger = puts/applies/administers
• borer = drills

In Danish, the present tense is often formed with -r.

The sentence can describe:

• something happening now
• a routine/procedure
• a general present situation

That is very normal in Danish.

Because før introduces a subordinate clause.

In Danish:

• main clauses usually have verb-second word order
• subordinate clauses usually keep subject + verb order

So:

• hun borer = she drills

After før, you keep that normal subordinate-clause order:

• før hun borer i tanden = before she drills in the tooth

Compare:

• Tandlægen lægger lokalbedøvelse.
  Main clause: verb comes early.

• Før hun borer i tanden, lægger tandlægen lokalbedøvelse.
  After the fronted subordinate clause, the main clause shows inversion: lægger tandlægen.

Because the dentist is being referred to as she in this sentence.

For people, Danish normally uses pronouns based on natural gender:

• hun = she
• han = he

So hun tells you the dentist is female here. You could also repeat tandlægen, but using a pronoun is more natural once the person has already been introduced.

The preposition i here means something like in or into.

With bore, Danish often uses bore i noget when talking about drilling into a thing:

• borer i tanden = drills in/into the tooth

This is just the normal Danish pattern. English may simply say drill the tooth, but Danish often prefers the preposition.

Because the sentence refers to a specific tooth being worked on.

So:

• tanden = the tooth

Compare:

• i tanden = in the tooth / into the tooth
• i en tand = in a tooth (any tooth, not a specific one)

Just i tand would not be standard here.

The comma marks the start of the subordinate clause:

• før hun borer i tanden

In Danish, many writers use a comma before subordinate clauses like this. You may also see sentences without that comma, depending on the comma style being followed. So the comma is there to show the clause boundary clearly.

No. Modern Danish does not capitalize all nouns.

Tandlægen is capitalized here only because it is the first word of the sentence.

So:

• Tandlægen lægger lokalbedøvelse.
• Jeg taler med tandlægen.

In the second example, tandlægen is not capitalized because it is not sentence-initial.