Insecticidal Soap

Southern gardeners have been using a soap and water spray for over a hundred years. One to three tablespoons of 'Kirk's Castile' soap is collected from a cheese grater and then dissolved in a gallon of water—it may take a day or two to dissolve completely. Once it is dissolved, shake the contents and pour it into a spray bottle. You must spray generous amounts. You might need to repeat this process every week because of newly hatched bugs. I have found this to be very affective on aphids and other soft bodied insects.
The only place I have found Kirks Castile Soap is at Publix.
If this process is too much for you new just go and buy some commercial insecticidal soap, which would be available at most big chain stores.

The best type of soap for killing insects is debatable; some recommend pure castile soap like me, but others endorse various name brand liquid dish liquids (most often Dawn and Ivory). Detergents are good choices because they are not affected by minerals in hard water, unlike non-detergent soaps. However, detergents have been known to be more damaging to plants if used excessively. If you choose to use a dish detergent, make sure to rinse your plants within an hour of applying the insecticide. Also, do not spray plants on very hot or humid days, as the plant will be more prone to burning. Always test a small area of the plant that is not too visible before applying and insecticide.