According to most plumbing codes a water softener drain line must not be connected directly to the household waste system. This is to prevent non-potable water from flowing backwards possibly mixing and contaminating potable (drinking) water. By code Water Softeners must be emptied into a laundry sink, floor drain, sump hole or properly trapped special outlet, preserving an air gap of at least two times the diameter of the drain line, but in no case less than 1-1/2" above the top of the receptacle used. In addition, the end of the drain line should be secured so that there is never any chance that it can become immersed in waste fluids or it can spray water into the surrounding area.
Plumbing your drain line into a laundry sink is probably the easiest and most convenient way, just secure the line 1 1/2" above the rim of the sink and you're done. Make sure to not leak the stopper or anything else in the laundry sink. The next easiest way is to run the drain line to a floor drain as long as you have a way to secure the end point 1 1/2" above the grill. My favourite is to run the drain into a drain stack just be sure to maintain the air gap.
Whenever there isn't a way to connect to a laundry sink or into a floor drain you can use an Air Gap Fitting and drain over head to plumbing from above the install location. These Air Gap Fittings are plumbing code required whenever you hard plumb the drain line (waste line) of water treatment equipment to your household plumbing. Verneco Water Softener Air Gap.
These need to be installed with a "p" trap to ensure no sewer gases enter the household.