Use a weed trimmer to remove as much of the foliage surrounding the grapevines as possible. Pests like to eat the grape vines, but many do not actually live on the vines themselves. Cutting down surrounding shrubs and grass will help to diminish the current pest population. This is especially important during the winter months since cutting down the foliage will actually prevent new infestations from occurring.
Examine the grapevine for leaves or branches that have excessive pest damage. Cut off these sections of the vine using pruning shears. Removing these damaged sections will remove some of the smaller pest populations, such as mites. It will also direct the plant's nutrients into the other healthy parts, which will strengthen it.
Spray the foliage of the grapevine with a liquid insecticide that is specially formulated for fruits and vegetables. These sprays usually come in spray bottles, but can also be placed into a garden sprayer for ease of application. Make sure to spray both the tops and bottoms of the leaves, as well as the main stem of the grapevine.
Wait the number of days specified on the manufacturer's instructions and then reapply the insecticide to the leaves and fruit of the grapevine. The waiting period is usually between 10 and 14 days.