It takes time and patience and some good old fashioned muscle. The best thing is to avoid the situation in the future by removing rollers from the applicator immediately after painting.
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Cut off chunks of paint or stain from the applicator with a utility knife. Remove as much dried paint or stain as you can with the utility knife.
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Fill a bucket with paint thinner or mineral spirits. WD-40 will also work well for dissolving any remaining paint or stain.
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Submerge the roller in the bucket of liquid and let it soak overnight.
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Remove the roller from the bucket and shake off the excess liquid into the bucket. Use an old rag to dry off the roller and applicator.
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Place the roller in a vise with the handle of the applicator sticking out in front of the vise. If you do not have access to a vise, grasp the roller between your knees with the applicator in front of you. Pull the applicator straight out from the roller. You may have to twist the applicator back an forth while you pull, but the roller should eventually separate from the applicator.