Depends on the severity and location of the problem.
Is it one isolated location in the bore? Near the breach or muzzle?
If isolated, soak a patch in Evaporust and using a jag run it down to that spot and let it sit. I would use a slightly undersized jag or brush for this. Do not use a brush exactly for that gauge/caliber, I've often heard of folks getting then stuck.
I have also just plugged the flash hole an filled the bore. Let sit, pour off into an empty coffee can and then scrub with a mild abrasive.
I've only dealt with one rusty bore on a cheap used rifle. But I have used evaporust on other items. Others may give better advise on what to scrub with.
What type of smoothbore gun? Gauge/caliber?