Learn Hardcore Danish: Jeg bor ved siden af skolen.

"Ved siden af" is indeed used to say "next to" or "by the side of" something. It closely matches the English phrase "by the side of", but in Danish it is a fixed expression often best translated simply as "next to".

Why is "af" used here, and could we just say "ved siden skolen"?

In Danish, "ved siden af" forms a complete expression meaning "next to". You generally won’t see it split as "ved siden skolen" without "af". Even though "af" means "of" in other contexts, here it’s part of the whole phrase and not optional.

Is there any difference in meaning if I say "Jeg bor tæt på skolen" instead?

"Tæt på" means "close to", which is less specific. It indicates short distance, but not necessarily right next to something. "Ved siden af" emphasizes direct adjacency.

Does the word order ever change in this sentence, like in English where we can say "Next to the school, I live"?

In Danish, the neutral, most common word order is "Jeg bor ved siden af skolen." While you can alter word order for stylistic reasons or emphasis, it’s less typical to start certain short clauses like "ved siden af skolen" before the subject in everyday speech.

How do I pronounce "ved siden af skolen"?

"ved" sounds somewhat like "veil" without the "l".
"siden" is roughly "SEE-den."
"af" is pronounced like "eh" or a short version of "av" (depending on dialect).
"skolen" is like "sko-len."