If you need to resize a ring that's too big because you've lost weight or because you've received a ring that's not your size, there are several options. Some are temporary solutions, while others will permanently change the ring's size.
Use a fabric Band-Aid (not plastic) for a cheap temporary solution. Take the adhesive off one half of the bandage and place the sticky part on the inside bottom of the ring band. Use cuticle scissors or a similar tool to trim off the excess fabric. This modification should last for several weeks, even if the bandage gets wet. You could also try moleskin, or brush a little clear nail polish inside the ring, "Real Simple" suggests.
Purchase a plastic ring guard for a more durable and long-lasting adjustment and slip the ring guard inside the ring. The flexibility of the plastic will allow the ring to slide easily over your knuckle, and then fit snugly at the base of your finger.
Consider whether your problem is big knuckles or skinny fingers. If your ring is a snug fit over the knuckle but won't stay upright, check with a jeweler to see whether sizing beads, a soldered insert or another device inside the ring might help.
Have the ring professionally resized by a jeweler for a permanent refitting. The jeweler will typically use one of two approaches: the mandrel method, in which the ring is compressed with a mallet; or, if the ring needs to be substantially smaller, cutting and resoldering the ring carefully so that the work is seamless.