Get rid of these pesky weeds, most likely sandbur from your description, by spot-treating plants with a selective herbicide labeled for sandbur. Take a sample of the plant to your local lawn and garden retailer and talk with an expert there to obtain a positive identification.
A preemergence herbicide may be helpful next Jan. or Feb. to prevent the germination of sandbur seeds.
Along with eliminating the sandburs, strive to maintain a healthy, vigorous lawn by watering, feeding, and mowing as needed for the dominant type of grass growing in your lawn.
For more information, check your local library for a lawn care book specifically for your region.