What is the soil like?
What is the soils pH?
Is this a lawn area or a flower/vegetable bed?

Ranunculus repens - Creeping Buttercup. Method of removal, as for any unwanted plants, is to pull or dig them out. Notice it is growing in an area where the grass is sparse. Weeds such as this take advantage of clear soil so, improve the grass cover and the weeds will decline. The little plant top right looks like Cardamine hirsutum, another common weed and one which spreads fast by seed.

I use weed fabric. Everyone seems to bash it, but i find it really useful. I have included the link below so you can see what sort of stuff. People buy cheap stuff and get confused as to why it doesn't work. Make sure you buy heavy duty woven material if you do.

Thanks
Alan

Here is a link that might be useful: Fabric