I slide a small knife blade under the feather working from the front to the back. Need to be careful to not dig into the wood. Some glue residue/fletching tape will remain. I usually file that off, or put a piece of sand paper on a small flat stick and sand it off.
By the time I need to refletch, my wood arrows aren't in the best of shape, so I don't bother resealing the fletch area. Just glue on the new fletches and good to go.
If you're using aluminum or carbons, you don't need to be as careful removing the old feathers, though you don't want to scratch the surface. Can get almost all of the residue off with the knife blade. Good idea to give them a rub down with denatured alcohol before refletching.