A photo would help identify the weed. Otherwise, any lawn weedkiller or weed and feed product should help.

Probably what I have in mine, it's a swine to get rid of as it has roots with nodules and runners that produce other plants and they are very deep rooted. I am at present resorting to blanket weedkiller! See the following to check this is it.
http://www.first-nature.com/flowers/potentilla-reptans.php

Sounds like buttercups... I have that same problem.. :(

Hi Honeysuckle,I went to your recommended site and verified that this is indeed what I have, now for the weed killer. My neighbour spent a day on his lawn with a steel comb, combing and pulling it out, same neighbour who puts plastic flowers in hanging baskets, I think his chances of ridding it are near to nil.