I keep it pointed downrange for about 30 seconds to be fairly sure it isn't a hang-fire. If it's a bolt-action, recock it by lifting and dropping the bolt (without cycling) and then try to fire the round again. 9/10 times a misfired rimfire round will fire the second time, in my experience. If it still doesn't go off, wait a bit longer, and then extract it carefully. Make safe and dispose of responsibly.
I dislike dealing with misfires in a semi-automatic or pistol much more — be much more careful with these. Again, wait a sensible amount of time to be sure it won't go off, and then extract the round, taking care that your hands are positioned in such a way that if the round does go off, the recoiling action presents a minimal risk of injury.
As always, exercise total control over the muzzle of the gun so that it is pointed at a safe backstop.