Weedol or Roundup, any of the "systemic" weedkillers which are stated to be safe on grass.Trying to dig or pull the plant up is hopeless. It will grow again from even a very tiny bit of root left in the ground and the root always breaks easily,as well as being deep
Correction! Weedol kills grass as, no doubt, does Roundup. But it can be used away from lawns ( or on individual dandelions in a lawn, if you are very careful).
The answqer is to never let them go to seed (dandelion clock). I am clear of them even though neighbouring verges and properties have loads of them. As soon as I see a yellow flower I use a tool like a long knife and just go round it down to about 6 inches and then pull the whole thing out.
If you dig them up, they will come back but much weaker. When they do come back, dig them up again and again and eventually, they will get fed up, be too weak and die.
Some of the selective herbicides such as verdone 2 will also do a good job whilst not killing the grass.