To check for the presence of spider mites, hold a piece of white paper beneath the leaves of a plant, and gently shake the foliage. If tiny bugs fall onto the paper, there's a problem.
Start with a natural approach. First, discard infected leaves. Then wipe down both sides of the remaining leaves using a damp cloth; repeat every week or so as long as mites are present. This simple act removes mites, as well as the dust and webbing that act as camouflage for the pests and as a nest for their eggs. As an alternative approach, spray infected plants with a garden hose, which will dislodge mites.
Don't use traditional pesticides; gardeners often attack their plants with bug sprays, only to find their spider mite situation worsen. That's because these insecticides kill the natural predators of spider mites -- lady beetles, lacewings, and predatory mites among them. There are specially formulated "miticides" on the market, but because of their toxicity, you should consider these a last resort.
For more severe infestations on outdoor plants, consider biological controls such as introducing predatory insects. Many garden centers sell them.
If these methods aren't sufficient, or if the problem is confined to indoor plants where biological controls are not an option, try "soft pesticides" such as insecticidal soaps. Available at garden centers, these soaps shouldn't have long-term toxic impact on harmless insects, but they can eliminate spider mites on contact. They are sprayed directly on the mites and work by suffocating them; cover the plant thoroughly for effective treatment.
Heavily infested foliage is often covered with dusty-looking webbing -- at this stage, the damage is often irreversible, and the plant should be discarded.