It’s important to know that HEALTH is the first line of defense for any plant to resist any type of pest attack. That means healthy (biologically active, humus rich) soil, reliable watering, good fertilization, etc (note that OVER fertilization, especially with Nitrogen heavy fertilizer, will result in weaker plants and thus more pest problems).
In the case of an Aphid infestation, the first step is to spray the aphids off with a strong stream of water, or wipe them off with a wet rag. Believe it or not, the little buggers will STARVE to DEATH before they can make it back onto the plant! Once the population has been knocked down in this way, control can be established by regular spraying of an appropriate organic insecticide. Oils such as Saf-T-Side (Petroleum oil),
Green Light (Neem oil), and Organocide (Fish and Sesame oils) are contact sprays and work to smother soft bodied insects like aphids (also scale, thrips, mites, etc.). Insecticidal Soap works similarly and is a time-tested remedy. CONTACT means that the product must have contact with the insect in order to work.
It’s also important to pay attention to whether or not there are a lot of ANTS hanging around your plants. Ants harvest and eat the secretions (called “honeydew”) of aphids and cleverly herd and protect them from predators (like a rancher with his cattle!). Suffice it to say, this ant activity works against control efforts, so if there are ants, consider keeping them under control as well. Sprinkling Diatomaceous Earth (DE) around the base of plants is a common organic solution, as well as setting outdoor bait stations like the Terro brand.
Here’s an excellent link for more information: