Learn Hardcore German: Im Urlaub lese ich gern ein Buch.

In German, Urlaub is masculine (der Urlaub) and when you express “during” or “in the time of” something, you need the dative case after in. So you say in dem Urlaub, which contracts to im Urlaub. Saying in Urlaub (without an article) doesn’t work for this temporal meaning.

Why does the sentence start with Im Urlaub and then become lese ich? Isn’t German normally Subject–Verb–Object?

German main clauses follow the “verb-second” (V2) rule. If you begin with an adverbial phrase like Im Urlaub (position 1), the finite verb lese must be in position 2. The subject ich then comes right after the verb. That’s why you get:
1 Im Urlaub
2 lese
3 ich
…gern ein Buch.

What does gern mean, and why is it placed after the verb?

gern means “gladly” or “with pleasure,” and it indicates you enjoy doing something (“I like reading”). In German, adverbs of manner (like gern) typically follow the conjugated verb: lese ich gern = “I like to read.”

What’s the difference between gern and gerne?

There is no change in meaning—both mean “gladly.” gerne is simply a stylistic or regional variation of gern. You can say either ich lese gern or ich lese gerne.

Why is it ein Buch and not something else? What case is that?

ein Buch is the direct object of the verb lesen, so it takes the accusative case. For a neuter noun like Buch, the indefinite article ein looks the same in the nominative and accusative:
nominative neuter: ein Buch
accusative neuter: ein Buch

Could I express a more general habit by using the plural Bücher instead?

Yes. If you want to say “I like reading books” in general, you could say Im Urlaub lese ich gern Bücher. That shifts from “a book” (one book at a time) to “books” (books in general).