Die Babysitterin liest dem Kind eine Gutenachtgeschichte vor.

Because the verb here is vorlesen, which is a separable verb.

• The full infinitive is vorlesen = to read aloud / to read to someone
• In a normal main clause, the verb splits:
  • liest goes to the usual verb position
  • vor goes to the end

So:

• Die Babysitterin liest dem Kind eine Gutenachtgeschichte vor.

Compare:

• Ich lese vor.
• Sie liest dem Kind vor.

But in the infinitive, it stays together:

• Sie will dem Kind eine Gutenachtgeschichte vorlesen.

Lesen is the infinitive, meaning to read.
Liest is the 3rd person singular present tense form, used with die Babysitterin = she / the babysitter.

Conjugation of lesen in the present tense:

• ich lese
• du liest
• er/sie/es liest
• wir lesen
• ihr lest
• sie/Sie lesen

So die Babysitterin liest means the babysitter reads / is reading.

This is also an example of a stem-changing verb:

• lesen
• du liest
• er/sie/es liest

Because dem Kind is in the dative case.

In this sentence, the child is the person receiving the story. German often marks that receiver with the dative.

A useful way to think about it:

• Die Babysitterin = the subject, the person doing the action
• eine Gutenachtgeschichte = the thing being read
• dem Kind = the person the story is being read to

So:

• jemandem etwas vorlesen = to read something to someone

Here:

• jemandem → dem Kind (dative)
• etwas → eine Gutenachtgeschichte (accusative)

Because the sentence has two objects, and they do different jobs.

• dem Kind is the indirect object → dative
• eine Gutenachtgeschichte is the direct object → accusative

The direct object is the thing directly affected by the verb:
the babysitter is reading a bedtime story.

So the pattern is:

• jemandem (dative)
• etwas (accusative)
• vorlesen

That is why German uses:

• dem Kind = dative
• eine Gutenachtgeschichte = accusative

Because Gutenachtgeschichte is a feminine noun.

The noun Geschichte is feminine: die Geschichte.
In German compounds, the last part determines the gender. Since the last part is Geschichte, the whole compound is feminine too:

• die Gutenachtgeschichte

In the accusative singular, the feminine indefinite article is still eine:

• nominative: eine Gutenachtgeschichte
• accusative: eine Gutenachtgeschichte

Compare with other genders:

• masculine accusative: einen Hund
• neuter accusative: ein Buch
• feminine accusative: eine Geschichte

The ending -in is a common way to form a female person noun in German.

• der Babysitter = male babysitter
• die Babysitterin = female babysitter

So Babysitterin specifically tells you the babysitter is female.

This pattern is very common:

• der Lehrer → die Lehrerin
• der Verkäufer → die Verkäuferin

Yes. German very often combines nouns into one long compound noun.

Here:

• gute Nacht = good night
• die Geschichte = story

Together they form Gutenachtgeschichte = bedtime story / good-night story.

A very important rule for compounds:

• the last noun determines the gender
• the last noun also gives the basic meaning category

So because the last part is Geschichte:

• the whole word is feminine: die Gutenachtgeschichte
• the whole word is a kind of story

Yes, German word order is more flexible than English, but the case endings help show who is doing what.

The most neutral version here is:

• Die Babysitterin liest dem Kind eine Gutenachtgeschichte vor.

You could also say:

• Dem Kind liest die Babysitterin eine Gutenachtgeschichte vor.

That puts more focus on dem Kind.

But one thing stays the same in a main clause:

• the conjugated verb liest stays in second position
• the separable prefix vor stays at the end

So even if another element comes first, the sentence still keeps that basic frame.

That is a very common order when a sentence has both a dative object and an accusative object.

German often puts:

• dative object first
• accusative object second

So:

• dem Kind (to the child)
• eine Gutenachtgeschichte (a bedtime story)

This order sounds natural here.
Because the cases are marked clearly, other orders may be possible in some contexts, but this is the most ordinary choice for this sentence.

Because in German, all nouns are capitalized.

So in this sentence:

• Babysitterin
• Kind
• Gutenachtgeschichte

are all capitalized because they are nouns.

This is a basic spelling rule in German and applies everywhere, not just at the start of a sentence.

Because grammatical gender in German is not always the same as biological sex.

Kind is a neuter noun:

• nominative: das Kind
• dative: dem Kind

That does not mean the child is somehow “it” in a personal sense. It just means the noun Kind belongs to the neuter grammatical gender class.

German has many nouns for people whose grammatical gender does not directly tell you the person’s real-life sex:

• das Kind = child
• das Mädchen = girl

So here dem Kind is simply the correct dative form of das Kind.

A very useful pattern is:

• jemand liest jemandem etwas vor

or in dictionary form:

• jemandem etwas vorlesen

This means:

• someone reads something to someone / reads something aloud to someone

So you can build many similar sentences:

• Ich lese dem Kind ein Buch vor.
• Der Vater liest seiner Tochter eine Geschichte vor.
• Sie liest den Kindern vor.

If you learn the verb together with its cases, it becomes much easier to build correct German sentences.