Thanks for writing. My first tactic for dealing with aphids is to spray them off my plants with a strong stream of water from the garden hose every other day for a week or two. Once they're knocked off a plant, aphids don't often crawl back on.
If that's not working for you or you want something more powerful, you can use something like an insecticidal soap. You'll want to follow the directions on the packaging to know how much to use and how often to use it. Keep in mind that with aphids, persistence is key! They can reproduce and create a whole new generation in a week's time.
There are more powerful insecticides available, too --- both organic types that contain neem oil and other botanical agents, as well as synthetic products. If you wish to go this route, look for them at your local garden center or home-improvement store. Also: Make sure the product says it's for use on aphids before you buy it.
---Justin, Senior Garden Editor, BHG.com