once the seed heads have released their seeds, the stems can be collected and weaved into small baskets.

or the stems could be harvested earlier, but the first method is how to be sure you'll have more baskets next year!

it'd be great to get your soil tested or something to find out if the dandelions would be okay to eat, in time for the next round of lawn-mowing. the flowers can go into pancake batter for fritters, they can make a great honey substitute, the root can be baked & ground up to make a tea/coffee substitute, the leaves are great for salads, dandelions can do it all, lol

They are great for fertilizer.

You could gather the yellow heads and make a dye if you have any natural fibers around. It comes out to a sort of yellowy beige

Know any rabbit-owners?

Rabbits love dandelions, and they are good for their health :)

Honnestly if the road is not a very ugly busy right accross the backyard, I don't care. Field are alongside roads and actual truck go in it to take care of the plant. You decide if you backyard is too much dirty. Young plant are less dirty because they have grown for a short amount of time and dandelion doesn't grow over a few month.

Whatever you do with them, wash them.