I just stick it in my compost... cuz wood ash, can be pretty strong... doesn't take much. Plus, you need to make sure that nothing bad was burnt, like those store bought fire logs with chemicals in them... or some kind of starter log...
Just to give you an idea how strong wood ashes are, wood ashes, in the old days were used as lye to make soap.

Wood Ash is about 70 percent calcium carbonate, lime, and is souble enough to quickly raise your soils pH much higher than it already is. That change is not very long lasting and maybe, possibly if you put the wood ash on in the fall the adverse affects would not be very apparent by planting season. What is in your Indiana soil that makes it have a high pH?

Could wood ash be used to raise ph in a brassica bed? If so, how long before the brassicas went in should it be added to the soil? I currently spread ashes from my logburner on the gooseberries and blackcurrants. I haven't grown brassicas here yet - my veg plot is new this year, but I've done a soil test and my soil is borderline for brassicas - ph 6 or 6.5 so it doesn't need much to raise it a bit to combat clubroot. However, they'll be going in in a few weeks so I think I've left it too late this year? Would using wood ash be worth a try I wonder?

Because wood ashes are very alkaline they wil raise tyour soil pH and because that CaCo3 is so water soluble it will be for a short period of time. Wood ash is quick and fast but not long term. You would have to experiment to see how much is needed to raise the pH of your soil how far to determine how much you need.

Wood Ash in the Garden.
By Rosie Lerner,Extension Consumer Horticulturist

"The chilly winds of winter will likely keep many a wood-burning stove glowing, leaving stove owners with the ashes to dispose of. Many gardening books advise throwing these ashes in the garden. But what affect do these ashes have on the garden?Wood ash does have fertilizer value, the amount varying somewhat with the species of wood being used. Generally, wood ash contains less than 10%potash, 1% phosphate and trace amounts of micro nutrients such as iron,manganese, boron, copper and zinc. Trace amounts of heavy metals such as lead, cadmium, nickel and chromium also may be present. Wood ashes do not contain nitrogen.The largest component of wood ash (about 25%) is calcium carbonate, a common liming material which increases soil alkalinity. Wood ash has a very fine particle size which causes it to react rapidly and completely in the soil.So although small amounts of nutrients are applied with wood ash, the main effect is that of a liming agent.Increasing the alkalinity of the soil does affect plant nutrition. Nutrients are most readily available to plants when the soil is slightly acidic. As soil alkalinity increases and the pH rises above 7.0, nutrients such as phosphorus,iron, boron, manganese, copper, zinc and potassium become chemically tied to the soil and less available for plant use.Applying small amounts of wood ash to most soils will not adversely affect your garden crops and the ash does help replenish some nutrients. But because wood ash increases soil pH, adding large amounts can do more harm than good. Keep in mind that wood ash which has been exposed to the weather, particularly rainfall, has lost a lot of its potency including nutrients.Specific recommendations for the use of wood ash in the garden are difficult to make because soil composition and reaction varies from garden to garden. Distinctly acidic soils (pH less that 5.5) will likely be improved by wood ash addition. Soils that are slightly acidic (pH 6.0 to 6.5) should not be harmed by the application of 20 pounds per 100 square feet, annually.However, if your soil is neutral or alkaline (pH greater than 7.0), find another way to dispose of the wood ash. If you donÂt know the acidity or alkalinity of your soil, have it tested for pH.Crop tolerance to alkaline soil also should be considered. Some plants such as asparagus and junipers are more tolerant of slightly alkaline conditions than "acid-loving" plants such as potatoes, rhododendrons, and blueberries.Wood ash should never be used on such acid-loving plants"

Too much ash can increase pH or accumulate high levels of salts that can be harmful to some plants, so use ashes carefully. Wood ash has a NPK of 0-1-3