Your softener needs to flush out the nasty stuff it collects. That’s the drain line. Run a small flexible tube from the control valve to your drain.
You need an air gap here. This means the tube doesn’t touch the drain water. It just hangs over the sink or drops into a standpipe. This is not optional. It stops contaminated water from siphoning back into your clean drinking water.
Run the brine tank overflow tube to the same drain. This just catches any accidental water if the tank overflows. It’s a simple plastic tube, but it saves you from a very wet floor.
How To Install A Water Softener System at Lilly Hurdle blog