If you are talking about killing off a section of lawn to create a garden, then spraying with Roundup is the way to go.
The grass should look withered in about a week.
I suggest spraying twice, a few days apart, so you don’t miss any grass, it will be a weed in your garden.
Only use regular Roundup, not any long term, ground clearing, or season long formulas.
Just glyphosate, and any generic type is also ok.
And then you can also optionally cover the area with a clear tarp, and weigh down the edges with bricks or dirt, or buy some nice bagged compost and use those bags to hold down the tarp edges.
You do this after you turn over the dead grass, about a week or two after you spray.
You can turn over the soil with a garden fork or a rototiller.
Do not ever rototill live grass, it will be coming back up for years like a weed.
The tarp will heat the soil, this is called solarizing, it kills weed seeds that would otherwise sprout in your garden.