Brushed finish steel is made in exactly the same way as it sounds - by brushing it! At the factory it is usually done with a stiff nylon, fibreglass or possible soft-ish wire brush attachment on a polishing wheel. I'd recommend not using an electric device for home brushing though as the possibility for cock-up is pretty high! You can repair small areas of damage (tiny scratches, etc) using a fibreglass pen designed for the job (check out eBay), and for slightly larger areas you can us a Scotchbrite pad. Just go gently and in the direction of the "grain" and you get a pretty good result.

I'd definitely steer you clear of attempting to brush an entire watch at home as you will essentially need to dismantle the case and bracelet, but many jewellers will offer the service, and nowadays Breitling seem less averse to doing it if asked as part of a service.