Isolating a binding brake is fairly straighforward, most of which is reflected in the various answers above.

First loosen the cable at the calipers until they move all the way out from the rim. Remove the cable from the binding bolt but leave the housing in the barrel.

Second, push the two pads to the rim and release. They should offer a fairly large amount of resistance and spring right back when released. If not the pivots are tight or corroded. I doubt very much that lack of lubrication alone would cause calipers to not release.

If the calipers move freely check the cable. Hold onto the cable with one hand, about an inch from where it emerges from the barrel. Pull on the brake lever with your other hand - it should move very easily back and forth. If you don't have aero or sti style brake lever you can easily disengage the other end of the cable from the lever temporarily and move it that way. If it moves with difficulty remove the entire cable and check for dryness and corrosion. If there is ANY corrosion replace the cable and housing and use a light machine oil or teflon lube when you reinstall. Just because modern housings are lined with teflon does not mean the cable will not corrode - small spaces easily harbor water vapor.

If cable and caliper are fine that leaves the lever. It should always move VERY easily. If it does not there are various reasons it could bind. Too much to go into here, but careful inspection should tell you the problem. Good luck!