Small claims court gets pictured as a place for personal disputes — one neighbor against another, a friend who never paid back a loan. It works exactly the same way against a business, and a lot of people never think to use it that way.
A local business that took payment and never delivered the service, a repair shop that damaged something instead of fixing it, a company that refuses to honor a warranty they're legally bound to — all of these are just as valid in small claims court as any dispute between two individuals. The business doesn't get special treatment just because it's a business instead of a person.
The process is the same either way. File the claim, name the business correctly (usually its registered legal name, not just the sign out front), pay the modest fee, and the business gets notified the same way an individual defendant would. Many small businesses settle before the hearing date once they realize a formal claim has actually been filed, since most would rather resolve it than spend a morning in court over a dispute they'd likely lose anyway.
Don't assume a business is too big or too official to be sued this way. For a huge range of everyday disputes, the process against a company is exactly as accessible as the process between any individual.