The insects that resemble tiny white spiders on potted plants are actually spider mites, which are insects you can control by hosing off the plant and removing the top layer of potting soil from the plant. Repeat the process several times if necessary. These insects do not usually require chemical control and do not cause serious damage to healthy plants.
If a spider mite infestation is severe and does not respond to washing the insects away, choose a mild, soap-based insecticide or neem oil. Cover the entire plant with the insecticide, including both sides of the leaves. These insecticides are only effective with direct contact with the insect.
Spider mites grow to about 1/20 inch in length, making them difficult to identify without magnification. Their bodies are white, yellow, red or green and are observable as they move across the foliage of the plant or as clusters on the underside of leaves. They often form webs that cover the plant and surrounding soil.
Spider mites feed by inserting their mouth parts into new growth of the plant while it is still tender. They use these parts as a straw to draw the cell contents from the plant. While damage is generally minor, an infestation can result in spots on the foliage or an occasional leaf turning yellow.