Certified GKH Gardening Expert
This can be difficult to do, but a selective crabgrass herbicide will do the trick. Just make sure to treat the current grass, and use a pre-emergent for the seeds before they pop next season.
If you want to do this without chemicals, then I would suggest using boiling water to kill the whole area and start over! You may have to do this a few times over the course of a week, but it will kill off all plants and pests in the soil.