To unstick a stuck brake caliper you'll need to remove the brake caliper from the vehicle.
Then use some old brake pads and a C Clamp to compress the brake calipers piston or pistons back into the brake caliper.
If the brake calipers piston does not move when you use a C Clamp then the brake caliper is bad and should be replaced.
However if the piston on the brake caliper does move with the C Clamp then it may work just fine afterwards but you should still plan on replacing the old brake caliper with a new one soon.
You can also spray some lubricant on the Calipers Piston such as WD 40 or PB Blaster or penetrating oil to help keep the caliper piston from sticking.
In some cases though it may be best to just put a new brake caliper on if you can afford to do so.
Also sometimes pressing the brake pedal in and out can sometimes release the brake caliper piston after lubricating it.
Remove the caliper from the disc, and pump the brake pedal to move the piston past the corroded portion.