So Olga and I find ourselves out in our yards together, digging up the dandelions, and wishing we knew about making good dandelion wine. We shrug our shoulders and say, what can you do? while knowing that we're really very fortunate to live across the street from such a lovely green space when so many on our planet live in cities so crowded it's hard to find nature at all.
I remember too well the days of weed bars and Killex... and I'm so glad that our society is wising up when it comes to using poisonous chemicals to "improve" our environment by eradicating pesky weeds. But at the same time, there are lots of things I'd rather be doing than digging up those tenacious dandelions and tossing them in the trash. They're almost impossible to compost unless you have a really hot compost pile that kills even dandelion roots, leaves and seeds... as well as beneficial composting bacteria.
So here's an idea from Ron Berezan, the Urban Farmer who used to live in my city. He suggests that rather than tossing those dandys into the garbage for the City to deal with, put them in a container full of water. Leave them in there until they drown (read, turn mushy and soft and sink to the bottom) and drain the liquid, which by then is an excellent compost tea. The mushy stuff can then be composted. Keep in mind that it's important to keep a lid on things -- to keep mosquito populations down and to contain the "fragrance" of the process.
Of course, if you don't like digging, and this method of composting dandelions seems too onerous to you, perhaps the best thing is to learn to like dandelions! Or dandelion salad...