I put manure into a big steel trough, cover it with water and let it turn into a smelly brew. Then I bucket that over crushed biochar and let it soak for a week or more. Sometimes I use seaweed if I've got it handy (beach is 45 minutes away, so not always). I've also started putting it directly into compost bins as I add material.
I mix it in with the chickens' bedding and sprinkle it in their run. Mainly I do that for odor-control, but it works to inoculate the char at the same time.
If I ever get to the point where I'm producing too much char for that (a girl can dream), I'll probably just spread it in the fall in whatever area I'm planning to put beans the following year. Beans aren't bothered by the nutrient draw-down of un-inoculated char. That gives the char a full year, plus a little, to inoculate itself. Plus it minimizes the number of steps I have to take it through manually. I like simplicity.
I do what Ellendra does plus one other labour-saving trick: I let the chickens eat as much biochar as they want, since they free range in the area where I produce it. Now most of the chickenpoop around the place is black, including what they leave in the coop.
Running it through livestock (or worms) is perhaps the ultimate inoculation and application method.