There are many reasons that a ring finger can become so swollen, that any attempt to remove a ring will be fraught with disappointment. In case of an accident, whereby the finger is swollen, it must be removed to reinstate a normal flow of blood to the affected finger.
Another way a finger can get swollen is by eating certain substances, such as sodium, which will swell the finger to the point of not allowing any ring to be removed. Most people will like to try any means to remove a stuck ring, then to have the ring cut off.
In one of the links spraying the affected finger with Windex will loosen the ring enough to remove a stuck ring. Another method called the undertaker ring method requires using an elastic oxygen mask strap.
The method calls for wrapping the affected finger tightly with the elastic strap, then threading it underneath the stuck ring and being able to remove the ring that way.
Neither of these methods should be attempted if there is an injury on the finger, or if the patient cannot handle the pressure of the wrapping up of the finger.
If neither of these methods work, as a last resort, you might have to have the ring cut off in a hospital, or sterile medical setting.