If chemical control is your thing, spot spray with a standard broad leaf herbicide. However, the chemicals in many pesticides are increasingly being found to be at the root of many health issues. Children and pets are especially vulnerable to lawn chemicals.
To physically remove existing ground ivy, rake it to raise and expose the runners, then mow it as low as possible.
An organic weed control program would suggest looking at the infestation holistically. Ground ivy tends to loves moist, poorly drained soil so you could try and alleviate the problem by aerating and watering as little as possible. You could also improve the composition of the soil through topdresssing combined with some overseeding to give grass the competitive advantage.