Your Spider Plant need a bright but indirect sunlight location.
Water only when the soil is dry. Too much water can cause the plant to decline and even suffer root rot.
Spiders can also be sensitive to conditioned water. Using distilled water can be appreciated by a Spider Plant.
It is a good idea to remove the off shoots into there own pots as they can put a strain on the parent plant. Reminds me of motherhood!
This link will refresh you on the care requirements.