Most organic grub control for vegetable gardens is done through biological controls. Anything from chickens in the garden to microbes and predatory insects will reduce grub populations. Using a combination of these methods is the most helpful, since all of them are based around controlling the population of problem pests, not eradicating them entirely. Tiny populations of grubs may not be worth the expense to control, but large infestations generally mean there's a serious lack of natural grub predators in your garden.
Beneficial nematodes are available for purchase from garden centers and direct from manufacturers. As a biological control, they have a very short shelf life, so obtaining them from the manufacturer is preferable. Steinernema and Heterorhabditis genus of nematodes are the ones generally used for grub control. It's easier to decide which to use if you can identify the grub species you're dealing with. Often your local garden center can help with grub identification.
Milky spore disease (Paenibacillus popillae) is a commercially available microbe insecticide that must be applied when soil temperatures are between 60 and 70 degrees Fahrenheit. Initial control can take more than a year, but will last up to 30 years if allowed to persist. Not only is milky spore disease compatible with other beneficial soil-borne microbes, it has also conclusively been proven to work fine with the parasitic Tiphia wasp, which also preys on grubs.
Tiphia wasps (Tiphia vernalis) were released in the eastern U.S. from 1925 through 1953. They require an adequate grub population to establish after a release, as well as nectar- and honeydew-feeding trees such as elm, pine and poplar. The adult Tiphia feeds in the shade of these trees on the honeydew left behind from feeding aphids. A single female wasp lays eggs on up to 80 grubs in a few days, killing the grub and continuing the Tiphia life cycle. Contact local extension services to find out more about planned local Tiphia releases.
Adult stages of grubs may be hand-picked from the garden in the morning and evening, when they are less active. Most of these are various types of beetles (such as the Japanese beetle, Popillia japonica) and June bugs (genus Phyllophaga). Obtain a list of all the usual suspects from your local nursery to help you identify the adult culprits on site. Drop them into a bucket of soapy water to kill them. Skip the soapy water and feed them to your chickens for protein.
Extensive use of chemical insecticides, salt-saturated chemical fertilizers and toxic herbicides will dwindle populations of beneficial insects and microbes. Oftentimes, the beneficial organisms have a harder time dealing with these products than the grubs do. Not many species of vegetables attract grubs in the first place. Research the common pests of plants that you want before planting them so you can choose whether the plants you want are worth dealing with grubs.