I found the following from the Univ. of CA, Davis:
Mike

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Wood Ashes as Fertilizer
 There has been considerable talk lately of recycling yard prunings and clippings as mulches and composts. Another source of recyclable materials is the ash from the fireplace or barbecue. At one time wood ashes were a chief source of potassium and much used in farming and horticulture. While not an important fertilizer anymore, gardeners with a supply of ashes often want to know if they would be useful as a fertilizer or soil amendment.
 The answer is yes, if used appropriately. The benefits derived from ashes depend on your soil and the rate at which the ashes are applied. Generally, ashes contain potassium, a major plant nutrient plus a number of minor nutrients. Wood ashes contain all the mineral elements that were in the wood, except for nitrogen and sulfur which are lost through the burning process. Potassium, calcium and magnesium carbonate or oxide are present in comparatively large amounts giving the ashes a strongly alkaline reaction which can neutralize acid soils. However in soils that are already alkaline, high application rates can be harmful. A further compounding problem is that about 80 to 90 percent of the minerals in wood ashes are water-soluble, so that high application rates can cause salts to build up in soils, resulting in plant injury.
 As a plant food, ashes contain 5 to 7 percent potassium and 11/2 to 2 percent phosphorous. They also have 25 to 50 percent calcium compounds. Hardwood (e.g. oak) ashes contain more potassium than those from softwoods (e.g. pine). If left out in the rain, because these nutrients are water-soluble, the ashes will lose their nutritive value. The less soluble carbonates which cause alkalinity will remain longer.
 So how to use ashes? An average application is 5 to 10 pounds per 100 square feet, scattered on a freshly tilled soil and raked in. For a pre-plant treatment, it is best to apply ashes 3 or 4 weeks in advance of planting. They also can be sidedressed around growing plants or used as a mulch. A ring of ashes around a plant may ward off snails and slugs because the ashes are irritating to them.
 In order to avoid problems of excess salinity or alkalinity, the applications should be limited to once per year. Avoid contact between freshly spread ashes and germinating seeds or new plant roots by spreading ashes a few inches away from plants. Ashes that settle on foliage can cause burning. Prevent this by thoroughly rinsing plants after applying ashes. Because they are alkaline, avoid using ashes around azaleas, camellias and other acid-loving plants.Â
 Remember that ashes contain very little nitrogen, so your plant's need for this element must be met by other sources in a regular fertilizer schedule.

We always scatter the fireplace ashes around the yard each time we clean out the fireplace. Just a thin layer around the yard really greens up the grass in winter. Make sure that you are using only hardwood ashes and not treated wood or leftovers from those fake firelog things.

For grill ashes, I don't know. Again, make sure what kind of chemicals are left behind from the charcoal before you put them into your garden soil.

We use a plastic bucket with holes punched in the bottom, so that we just walk around the yard and shake to disperse the ashes (make sure they are cool first).