The Mysterious Fan That Sounds Like a Jet Engine

My computer’s fan has suddenly become extremely loud, sounding almost like a jet engine, even when I’m only doing light tasks. I’ve checked that the vents aren’t blocked and restarted the system, but the noise continues; how can I find out whether this is caused by dust, overheating, a background process, or a failing fan, and what safe steps should I try before taking the computer in for repair?