Your lawn is being invaded by weeds. The problem is how to remove the weeds without killing the grass. By first improving the health of your lawn and then removing the weeds this can be accomplished.
Improving Lawn Health
Aerate the soil to deter weed growth. Weeds flourish in dense, compacted soil. Aeration can be accomplished by using a lawn aerator. Walking your lawn while wearing spiked shoes will work for a small yard.
Mow the grass often. Leave the grass about 2 1/2 inches tall to provide shade, which will inhibit weed growth. Keeping the yard mowed prevents weeds from developing seed heads. Rake up grass clippings if they contain any weed seed.
Combine 1 cup liquid dish soap and 1 cup ammonia in a 20 gallon hose-end sprayer and spray your yard thoroughly every two to three weeks. This soap bath will improve the health of your lawn. Clean grass blades will allow fertilizers and herbicides to penetrate the grass without interference from dust and oils.
Fertilize the yard to obtain a lush, healthy lawn. Thick grass creates a less desirable environment for weeds to grow in.
Use a long screwdriver or knife to dig deeply around the base of each weed. Pull the weed from the soil. Discard weeds to prevent reseeding.
Spray each weed with a commercially prepared organic herbicide that is safe for lawns. An alternative organic solution is to mix 1 gallon apple cider vinegar with 1 tablespoon liquid dish soap. Spray this directly on each weed.
As an alternative to an organic herbicide, a commercially prepared broadleaf weed killer can be applied, following the manufacturer's directions.