If the mother plant is in a hanging basket, cut off a plantlet, pin it to the soil of the pot that will be its home. Water it well and put the pot in a plastic bag or under a plastic dome to preserve the humidity. Keep the new plant out of direct sun and ventilate it briefly each day to prevent fungus problems. When new leaves form, remove the cover. My spider plant gets brown tips on the leaves no matter what I do.
Spider plants are sensitive to the chemicals in tap water.
It should always be watered with distilled water, rain water, reverse osmosis water, melted snow or water collected from a dehumidifier. Once you have changed the water source, all the new leaves should be normal, but you will have to trim the brown tips off the old leaves. There are webs under the leaves of my plant and the leaves look dull and rough. Your plant has spider mites. They attack when the air is hot and dry.