First off, try a good fertilizer (buy a bag of the weed n/ feed type at the hardware store or Costco, etc). Toss some of that on all over (follow the directions on the bag). Also, if you have not aerated your lawn in a while, I would suggest paying the $25 to have some local do it for you. We get flyers on our door for it, and I have been known to hit up people in the neighborhood when I see them aerating someone else's yard. We do this once per year. Be sure to mow your lawn on the highest mower setting. This keeps the soil more moist, which will require less watering on your part, and a healthier lawn (which will help suffocate the weeds).
The only REAL success I have had for Dandylions though is removing them. Wait until after a good rain storm (hopefully this weekend), to soften the soil, then grab one of those little handheld shovels, and dig them up. I dig adjacent to the weed - about an inch or two, lift the soil/weed/grass up about an inch, and then you can usually just pull the weed right out. Then pack the remaining sod back down, and you'll never really even notice there was a weed there. I do this every year to my neighbors yard, on my side of their yard, and it does wonders at keeping them at bay. If I did the other side of their yard, I could likely erradicate them completely. Try of course to get them before they seed.
If I'm in a hurry - don't have my shovel, etc - and I see one in my yard, I immediately pick off the little flower and seed pods burried deep down in the base of the weed, before they have a chance to bloom (since I can't pull the weed completely without the shovel). They will eventually come back, but it's a good temporary solution to keeping them from spreading that day or the next until you can pull it out.
Clearly, I'm a bit OCD about this, but you asked. ;)