The answer to 'how to unclog water softener' is to first check the brine tank. If the tank is full of salt, it may have become compacted and clogged the system. Start by removing any excess salt from the tank and then run a regeneration cycle to flush the system.
If the issue persists, you may need to clean the resin bed in the softener tank. This can be done by disconnecting the softener from the plumbing, removing the tank, and using a garden hose to backwash the resin. Be sure to follow the manufacturer's instructions carefully during this process.