Very pretty to look at in all their yellow splendor, but once that's gone what's left is all those seeds waiting to pounce.
Somewhere I read about a homemade solution to eliminate them. Kill is such a harsh word, but that is the bottom line.
Something along the lines of dishsoap and vinegar perhaps. Any recipes out there to share? 
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Hope I'm not too late on this post, but there's a few ways to go about killing those little pests. Vinegar definitely works, but only temporarily. And no matter what, the dandelions will most likely come back. My homemade solution is:
1. Boil water, the heat will kill the dandelions and get them loose, but probably won't kill anything else, especially a lawn.
2. Get yourself a forked hoe and try and get the VERY bottom roots. Once you get the root out, try to fish the rest of the pieces out and any visible seeds; this takes a lot of effort, but pays off once the task is completed.
3. Replace or fill any dirt you need to with a layer of mulch, this will help your other plants/lawn while blocking the weeds from getting sunlight.
4. After this is all said and done I DOUSE the soil with 5% vinegar, as this again won't kill a lawn.
Keep strong girl!