Around here, if you till up the ground the grass will pop up even worse. I buy round-up in the fall when they discount it at Tractor supply. They have a 2.5 gallon jug.Then I use a 2 gallon pump up sprayer. I have to touch it up with more round up about every 6 weeks. It works best when it's hot and dry.
If I want to leave the grass and just kill the weeds I use Grazon. Grazon will also kill small trees! Yes!