PUT IT IN YOUR COMPOST!!! Mix the wood ash into your compost heap, which can be a mixture of anything you have around you, such as chicken and rabbit manure, straw, shavings, kitchen scraps, leaves and yard rakings, newsprint and any other organics. The outcome is a neutral pH compost, but always check it.
Wood ash tends to be alkaline and is appropriate for plants like lilacs that like sweet soil. I wouldn't apply too much in any one area.
Besides lilacs, lavender also could benefit from pH reduction if your soil is very acidic.
It affects soil pH relatively rapidly, so use sparingly as it may be too much for the plant to handle.
It's also a good source of phosphorus. Mix it into the soil of your vegetable garden, on perennial beds, and under any shrubs or that are not acid-lovers.
Another use for ashes if you'd like to CHANGE the COLOR of your hydrangeas from blue to pink or from baby pink to deeper pink or even scarlet/burgundy if they already dark pink. They are highly water soluble and will work right away. One application in a winter (over the snow is OK), another in a mid-May and one more in June and you'll change hydrangea color in a one season.
Put it around your rose bushes. Even peonies and tall bearded iris, lavender, clematis, columbine, lupine, rosemary, baby's breath, oriental poppies, daffodils, collard, broccoli, cauliflower, brussel sprouts, and cabbage also benefit.
Reminder, to have ashes in May and June you have to keep your winter ashes in a some close container away from the elements, otherwise they'll dissolve.
Wood ashes also discourage slugs and snails - it works like diatomaceous earth. It has a caustic action ( lye was made from ashes).