A water softener has two tanks, a resin tank and a brine tank, both of which can be very heavy when full. The keys are engaging the bypass valve, disconnecting the plumbing cleanly, and emptying the salt and water so you are not lifting hundreds of pounds.
Pro tip: Even drained, the resin tank retains significant weight from the resin beads, so plan for a heavy lift.
Watch out: A full brine tank and a water-filled resin tank are extremely heavy, so empty as much as possible and use a dolly.