How do we get rid of an entire lawn of crabgrass?

The front lawn of our new house in Utah is composed entirely of crabgrass. Obviously, we want a decent lawn, but don't know the best way to get rid of the one that's there now. If we just plow it under and plant new grass on top, will the crabgrass come back? Do we poison it, then plant new grass and will it still come back? Do we just lay sod over it and hope for the best(jk)? HELP!

Kill the old grass first. Round-up works well because it will not hurt they new grass seed. After the old grass has died, till the soil. Rake the yard and then water an inch or so. The watering will help the soil to settle (compact) some. When its dry, sow the seed. Hydroseeding works well. Or rent a slitter-seeder. The hydroseeding contains fertilizer. If slit-seed, put down some starter fertilizer.
Cover with straw. Water 1/2 hour, twice a day.