I use chunks that have not been soaked. I just drop them on top of the coals shortly after lighting via the Minion Method. Some people have mentioned they mix the lump among the unlit coals which would extend the smoke without attention.
I can find large bags of hickory & mesquite at Home Depot so check there (or whichever home improvement stores you have nearby) for the basic woods. Other woods like oak or fruit woods could be obtained from tree trimming companies, construction scrap (make sure it's untreated), or people who own orchards. If you find someone cutting down or pruning a tree they may be open to donating to your cause. You'd just have to be able to convert it to chunk sized pieces and be willing to wait while it dries & cures.
Joe