Learn German: Sie verbessern Ihre Aussprache, indem Sie sich den Text laut vorlesen. - You improve your pronunciation by reading the text aloud to yourself.

The conjunction indem expresses the method used to achieve something. While English uses "by" plus an "-ing" verb ("by reading"), German uses indem to start a full subordinate clause. This means it needs a subject (Sie) and a conjugated verb pushed to the end (vorlesen).

Since vorlesen is a separable verb, why isn't it split into lesen ... vor?

Because indem introduces a subordinate clause, the conjugated verb is pushed to the very end of the sentence. When a separable verb is forced to the end of a clause like this, its prefix (vor-) and its stem (lesen) reattach and must be written together as a single word: vorlesen.

What is the purpose of sich in this sentence?

The verb vorlesen means "to read aloud to someone." Since you are reading the text to yourself, you need a reflexive pronoun. Because the direct object being read is the text (den Text, Accusative case), the person receiving the action takes the Dative case. For the formal Sie, the Dative reflexive pronoun is sich.

Why is laut used instead of an adverb like "loudly"?

In German, adjectives like laut (loud) double as adverbs (loudly) without needing any special endings like the English "-ly". Here, laut simply acts as an adverb directly describing how you are reading the text.