You do not want to till live grass into your garden. Decide in the fall where you want your plot to be. Spray the area with a nonselective herbicide to kill grass and weeds. (Contact your local Extension office for herbicide recommendations.) Then remove the dead plants and till the ground. If the weather remains warm, weed and grass seeds in the ground may germinate, and you will want to reapply the herbicide. These actions will give you a jump start on your garden before spring.
It would be a good idea to do a soil test, stating that the area is for a vegetable garden. Contact your local Extension office for instructions. The results will include recommendations on any nutrients that should be added. Good organic compost is always a good additive to till in, as it will help retain moisture and add nutrients.