If tiny bugs are flying around your houseplants, they're most likely spider mites or fungus gnats. These pests reproduce in the soil, and when the population gets large, the damage to your plants becomes noticeable.
Spider mites thrive in heat and low humidity. The signs of spider mite damage on your houseplants include a yellow stippling of the leaves and webbing on their undersides. Turning down the heat and plugging in the humidifier can solve the problem, but this might not prove practical in the wintertime. Regularly washing off the leaves and using a horticultural oil can also remove the infestation.
Large numbers of fungus gnats feed on the roots of houseplants. You can see them running across the soil and leaves of your plants. They may even fly around the windows. Fungus gnats lay their eggs in organic-rich soil. To get rid of the adults, hang yellow sticky traps among plants to kill them. Let the soil dry out between watering to kill the larvae. Another solution is applying Bti (Bacillus thuringiensis israelensis), which is commonly used for mosquito control and sold at gardening centers.
Rather than spending money at the garden center, try a homemade solution. Shave a one-inch piece from a bar of Fels-Naptha soap into a quart of heated water. Stir until the soap dissolves and pour the liquid into a jar. Nearly fill a one-quart jar with water and stir in a teaspoon of the soap concentrate. Add a quarter cup of rubbing alcohol. Pour this solution into a spray bottle and spray the plants, including the underside of the leaves.