A couple of things to look for :
On most single actions you can remove the cylinder pin from them by sliding it forward. There is typically a latch to prevent that from happening so expect to push a latch pin to the side or something simular. Remove the cylinder pin forward and the cylinder will roll out of the frame to the side ( usualy to the right side).
Once you have the cylinder out you can push the case out of the chamber with a brass rod if it is real tight, or a wood dowl should be sufficiant.
Check the barrel for obstructions - if you had a squib load there may be a bullet or two lodged in the barrel. After the squib load lodges its bullet in the barrel , a follow up shot will creat high pressure and rupture the case. (that is one possiblility as to what happened)
Make sure you are shooting the correct ammo in your gun. Many single action .22's came with both a .22LR and a .22 Magnum cylinder. If you have the magmun cylinder in the gun and shoot a .22LR in it, the case will rupture.
If this fails to satisfy your problem , take it in for checkup and repair.