Cover plants with floating row covers in the spring when the plants are still small and most prone to lethal damage. The covers prevent the pests from accessing the plants while still allowing in sunlight and air. Remove the covers before the plants begin flowering; otherwise pollinating insects can't reach them.
Clean the area around the garden bed, removing weeds that may harbor the pests. Both insects often spread to cultivated beds from nearby uncultivated, weedy areas.
Rinse aphids from the foliage of plants with a sharp spray of water. Concentrate the spray on the underside of the leaves where most aphid colonies congregate.
Prune out badly damaged or infested parts of mature plants. Pruning out damaged areas works especially well for thrips, since their damage to new leaves and buds is usually visible before the insects are.
Spray plants with an insecticidal soap, following package instructions. The soap only works on aphids and thrips while it is wet, so application as often as every three days may be necessary until the pest population is under control. Rinse the soap from the foliage 24 hours after each application to remove the old residue.
Lay sticky traps around the base of plants infested with thrips. The thrips are attracted to the traps, which helps manage minor infestations.