Drill a hole in the bottom of the container in which you are planning to repot the spider plant and cover it with a coffee filter.
Clean the container in which you will be repoting the spider plant and then fill it with all-purpose potting soil. Avoid filling the container all the way up to the rim. Instead, stop at least a couple of inches below. The best soil for planting a spider plant is one labelled as sterilised and pasteurised. Look for either of these words on the bag of soil before purchasing.
Carefully root out the spider plant from the original pot. A large amount of soil would be clinging to the plant when you remove it. With your free hand, brush off some of the excess soil. You can now go ahead and divide the plant into two or more sections. You can easily divide a spider plant by hand so there is no need to use a kitchen or utility knife for this purpose.
Sink a section of the spider plant in the hole that you drilled earlier. Make sure that the depth of the plant in the soil is the same as it originally was. Get rid of air packets by packing soil around the root ball of the spider plant.
Now slowly water the plant until water starts draining out of the hole at the bottom of the container. If you over water the plant, make sure you git rid of the excess water in a saucer placed under the container. Do not fertilise the plant for four to six months after you have re-potted it.