A small leak around a softener often shows up as a damp patch, a salt crust, or a stain on the floor beside the cabinet. The water may come from several places, and each one has a different fix. Your first job is to stop the water, and your second is to find where it started.
Shut off the water before you touch anything
Know where the main shutoff for the house water is, and whether your softener has a bypass valve. If you can close the supply to the softener, do so before you try to tighten anything. Keep electrical outlets and power cords clear of standing water, and do not work near a wet floor with a live plug nearby.
Sort the water by its source
Dry the floor completely, then place paper towel or a clean cloth at each likely point. Brine tank water often leaves a salty crust as it dries, while fresh water from a connection tends to leave a clean wet mark. Run the house water for a short period with the softener in service, then check the towels again. Work through the candidates one at a time so you know which one produced the mark.
The usual places to check
Look at the inlet and outlet fittings where pipe meets the softener body, and at any union or compression nut. Check the drain line connection and its hose clamp. In the brine tank, look at the float assembly and the overflow. If the brine tank is filling beyond its normal level, the float or the valve may be misadjusted. Check the seal where the control head meets the resin tank, and the connection where the softener joins the water heater or the line to the washer valve. Tighten a loose fitting only if you know it is a compression or union fitting, and do not overtighten plastic.
When to stop and call a technician
Stop and call a professional if the leak comes from a crack in the resin tank, from the control valve body or its internal seal, or if water is under the resin tank rather than at a connection you can reach. Stop as well if the leak returns after a tightening you did yourself, or if you cannot identify the source. Write down what you found and where, along with the date you first noticed it, so the technician can start from your notes.