Most people kill the grass with something like ground clear, kleenup, or roundup. You may need to apply it more than once to kill all of the weeds. Follow label directions and precautions.
The other way would be to dig out the current grass with a sod cutter, you can rent one, or a spade. Turn it upside down or put it in the compost. If it has a lot of weeds, do this when the weeds are not seeding. Your compost must get hot enough to kill the weed seeds.
You can cover the lawn with newspaper or cardboard or solarize. July and August the are best times to solarize. Solarization helps to kill non-persistant weeds and resolve some soil issues at least temporarily.
If the weeds are very bad, and they are persistant weeds or you have a severe problem with nematodes, your only choice would be soil sterilization. That is usually done by professionals. Soil sterilization will kill everything, plants worms and microbes for up to one year. The soil would have to be enriched after that before anything will grow.