My Method:

Before Planting: Plant Perennial and annual flowers nearby to attract beneficail insects that prey on aphids

At time of planting: cover plants with row covers, put a reflective mulch under your plants such as aluminum foil

While plant grows: spray twice a week with water to knock them off plants

Once infected: spray with a garlic or hot pepper spray, pick aphids off and drown in soapy water

After Harvest: Pull weeds that may harbor eggs

Other organic methods include: spraying with insecticidal soap, oil, neem or pyrethrum
sticky yellow traps, yellow pans filled with soapy water, keeping grass mowed around garden, fermented extract of stinging nettle, importing lady bugs, cinnamon oil sprays sabadilla dust etc...