Help a novice with dandelions

[fishfingersrus]

Recently moved into a new house. Our neighbours all have lovely green lawns, kept immaculately. Our lawn has been neglected and is covered in dandelions.
What can I do to get rid of the dandelions? Spray or use one of those dandelion extraction contraptions? What about the lawn afterwards?
Also have young children so staying off the grass waiting for seeds to take is not an option.

As a first action, take the flower heads off and keep taking them off. This will stop them seeding this year.

I'd dig them out (an old dinner knife works well if you don't have a gadget) and on my soggy lawn I fill the holes with lawn sand but soil will do if the holes are too big to leave.

Keep mowing it.

All the above are child/pet/wildlife friendly and no nasty chemicals involved!

yes, dig them out consistently. fertilize in the spring and fall.

Another vote for the old kitchen knife. Very satisfying. Don’t bother with an official contraption.

Yes, dig them out. I find digging them up when the ground is wet is easiest. They’re pretty easy to get out at the moment. Never let the flowers go to seed.
If you have little ones you can make a game out of who can gather the most flowers.

Thanks all. A day of dandelion extraction it is!