A ring can get stuck on your finger if you do not take it off nightly or at least every 3-6 months for proper cleaning at a jewellery store. If you struggle to remove a ring, need soap or spit to get it off your finger it is too tight and needs to be sized up to a proper size.
If your ring gets stuck first and foremost; do not put your fingers in your mouth. Particles of skin, dirt, food and bacteria are on your hands and most certainly in the crevices of your ring; not only is it unhealthy for you but it is impolite to expect the goldsmith or jewellery professional to touch your ring after you have licked it.
Try to use Windex to attempt to remove the ring first, spray it on the finger and see if the ring will slide off. Avoid using Windex with pearls, ammolite or opal because it contains ammonia it can potentially damage the stone. If the Windex doesn’t work the next solution is the string wrap method.
Wrap your finger with a string from the first knuckle down to the ring, push the string under the ring, pull the string and as it unravels it will push the ring off your finger.
If your finger is swollen from an injury, the skin under the ring has begun to break because the ring has been too tight for too long or you believe your finger may be broken then it is time to have the ring cut off. If a ring needs to be cut off and you have an injury, then it is usually best to visit an emergency room to have your injury treated. If there is no injury visit a goldsmith. If you attempt to cut the ring off yourself with wire or bolt cutters be aware you may harm yourself or damage the ring beyond repair.
Once the ring has been cut off wait at least 2 weeks for the wound to heal and the finger to return to a normal size, at this time you can then have your finger size checked and the ring repaired.
For a proper ring fitting see a jewellery professional; the width of the ring does affect the sizing and fit of a ring. If you have arthritic hands speak to your goldsmith about sizing balls which are typically not comfortable for normal ring wear, but are a good option for hands with oversized knuckles.