There is a granular product that you scatter on your lawn that kills broad-leaf weeds like dandelion without harming the grass. I forget the name, but I'm sure your local garden center will be able to tell you.
We are not allowed to use herbicide in this area. I pull them out as soon as I see them. Unfortunately this means I do garden rounds every day and pull weeds at least weekly. More often when it rains a lot.
The most environmentally friendly way to get rid of dandelions is to manually pull them out. Bring them to the kitchen, they make an excellent salad, pick them when they are young, no bitterness.There is no-alternatives, cut the flower first before it seeds and then deal with the roots by cutting it as deep possible with a sharp knife or a weed-puller! It is preferable to do it after a rain when the soil is humid.
If you do not use weed killers (and you shouldn't) or compel you to uproot, you can try one of the tricks well known by gardeners to weaken dandelions and phasing them out:
Tip # 1: Cut the clump of dandelions flush then sprinkle the place of salt.
Tip # 2: Sprinkle each foot of dandelions with hot water, or better with the cooking water (as hot as possible) pasta or potatoes.
Tip # 3: Spray white vinegar in the heart of each tuft of dandelion.
I'm afraid the most effective way to get rid of them is to dig them out. Next year, you can try using a pre-emergent herbicide containing isoxaben, which has proven effective on dandelions, but like all pre-emergents it has no effect on weeds that have already germinated.
If you are not averse to herbicides, you can use Roundup in your planting beds. For the lawn there a number of broadleaf herbicides that will kill the weeds but leave your lawn unharmed.
Thanks everyone. I am going to try without herbicides because of children and pets.
@Hollyscarlo we are not allowed to use certain herbcides here, but there is an eco-friendly product on the market called weed-b-gone that works pretty good, with a few applications and won't hurt the grass. Apparently it saturates the leaf with iron to suffocate it but has no effect on the grass, but may be different if being sprayed near your flowers. Good luck.
I'm always trying to do things without using toxic lawn chemicals too, because of the kids and pets. You might want to check into these products from Gardens Alive (http://www.gardensalive.com/) to see if any of them would work for you. I think natural products take longer to work, but I'm okay with that. ~M
If you haven't used herbicide or pesticide, dandelion leaves are delicious. I braise mine briefly with chopped garlic then steam covered for about 5 minutes.