Spraying with water does help a lot. You can mix garlic and water, filter it and spray it on the plant with a little dish soap added. This will get rid of any stubborn infestation.
Three tablespoons per gallon of water sprayed during late afternoon should kill the aphids. They dehydrated.
Pepper plants are sensitive. You don't want to damage the plants so it would be best to come back the next morning to rinse the leaves with clean water.
"Safer" is to use insecticidal soap. In fact, there is a commercial brand with that name. I've used that and "Concern."
I had good luck with one of those "poison" sprayers that you pump up. Of course, I just put water in it...but you can spray it on, right where the bugs are and kind of squish them at the same time. I found many more on the underside of the leaves, than the tops. Don't kill any lady bugs or their larva or eggs-they will really help.
Short term the best way(as noted by others) is insecticidal soap. Try not to use it during the hottest part of the day. A blast of water is also good. Besure to blast from all angles, including underneath.
Long term the best method is to encourage natural predators. The three best predators are, in order, tiny predatory wasps, syrphid flies and ladybugs (especially the larvae). You will have to look closely to see the wasps. They are tiny, some smaller than the aphids they prey on. Syrphid flies are the hover flies that seem to follow you around, hovering just out of reach. There are a great many species and they come in all sizes. Some of them mimic the colors of a bee as camouflage. In some parts of the country the larger ones are known as news bees because they hum as they hover and seem to be trying to tell you something. Adult hover flies live on nectar and pollen but in the larval stage they are voratious carnivores on aphids and other soft bodied pests.
Syrphids and wasps both need nectar and pollen in the adult stage so be sure to provide it in your garden. They prefer small flowers. Let some of your onions, celantro and carrots go to seed. Those are favorites of both wasps and syrphids. Having a small patch of weeds that are left untouched somewhere near your garden provides them with cover and the proper environment. Gardens that are completely free of weeds have few predators.