This looks like a type of pennywort or dollarweed, Hydrocotyle spp.
It is a warm season perennial weed that spreads by seeds, rhizomes, and tubers. Dollarweed thrives in weak, thin turf with excessive moisture. The first defense against dollarweed is to reduce moisture levels and modify cultural methods (i.e., proper mowing height and irrigation).
Here is some information from Clemson on this weed, https://hgic.clemson.edu/factsheet/dollarweed/
You will have to make some decisions. In flower beds, you can use a systemic vegetation killer such as glyphosate. This will kill everything. If you have desirable plants you will have to shield them and follow label directions.
In the lawn: if the lawn is over 50% weeds, you will have to consider total lawn renovation. This can be done up until mid-October. Test your soil (http://extension.umd.edu/hgic/soils/soil-testing), decide on seed, prepare the site for planting, and seed or install sod. Now is the time for lawn renovation for a cool-season grass such as tall fescue. Tall fescue grows best in full sun to partial shade. Fine fescue is recommended if the lawn is mostly shaded.
Here is our publication on Lawn Establishment and Renovation see page 7 and our website http://extension.umd.edu/hgic/lawns/lawn-renovation
Here is more information from our IPM Report page 3 https://extension.umd.edu/sites/extension.umd.edu/files/_docs/programs/ipmnet/13Oct11L.pdf
If you need to spot treat only, use a post-emergent herbicide now and next growing season as soon as you notice the weed. You can use a combination herbicide that contains the following broadleaf weed killers: 2,4- D, dicamba, and mecoprop (MCPP) or MCPA. Follow label directions as caution needs to be used around the roots of trees and shrubs.