Washington State Extension Stewardship Gardening gives some excellent advice:
Food scraps contain valuable nutrients that can be used to improve garden soils. Waste fruit and vegetables, peelings, coffee grounds, egg shells, bakery products, and many other leftovers can be safely composted using proper methods. These food scraps contain valuable nutrients that can be composted to produce a rich soil additive.
Unfortunately, it's not as simple as placing the egg shells directly in the garden. Washington State Extension recommends burying the food scraps:
Food waste can be buried in empty spots in vegetable and flower gardens. Use a shovel to make a hole at least twelve inches deep. Add three to four inches of food scraps to the bottom of the hole. Use a shovel to chop and mix the wastes into the soil to speed composting. Cover food scraps with at least eight inches of soil to prevent rodents and pets from digging them up.
How long do you need to wait? More info from Washington State Extension:
Buried food scraps may take from two to six months to decompose, depending on soil moisture, temperature, worm population, and food source. In good garden soil, leafy greens will break down in weeks while whole citrus peels may take several months in a loose and fertile garden soil. Wait a month or more if the soil must be tilled before planting. Annual plants may be planted immediately. Check areas with buried food scraps before tilling to make sure that undecomposed food does not come to the surface.
To be honest, I think it's a lot of trouble and prefer to compost my veggie/food scraps directly into my green recyling can, following Waste Management's guidelines, to be picked up weekly. I've seen too many animals dig up deeply planted bulbs, let alone food scraps. Also, I'd be concerned about attracting rodents, raccoons, bears (yes, I said bears), or other curious animals. I hope this helps!