Shake the finial very gently. This will indicate how well-attached the finial is to the bedpost. Most finials that you shake will have a slight looseness to them. Unscrew the finial to the left until it comes off in your hand, or pull the finial out of the socket of the bedpost by yanking it straight up.
Measure the width of the dowel once you've removed the finial from the bedpost. Purchase replacement finials that are no bigger than this dowel width, as otherwise they won't fit in the bedpost hole.
Cut a 1-inch piece of two-sided tape and wrap it around the dowel. If the dowel on your replacement finial is significantly smaller than the other dowel, you'll need to wrap several layers of two-sided tape around it.
Slide the tape-wrapped dowel into the hole. Press it down firmly and adjust it so it's straight. Allow the adhesive to set for an hour.