You could turn over the earth, but that's hard work and it's almost certain that the weeds and grass will reappear. It's best to smother the grass and weeds with a thick layer of cardboard or layers of newspaper (about 10 layers thick), and then top with fresh soil and mulch.

In your post, you don't mention whether you want to plant your flowers and herbs now or if you just want to prepare the beds for planting next spring, so I'll give you the two methods I've used for each of the two cases.

For planting this year:

First of all, mow the planting area, cutting all vegetation (grass and weeds) as low as possible. Now, outline and edge your bed. Then dig holes where you will be placing your plants. Make these holes almost twice as wide and as deep as the plants. Take cardboard and/or newspaper and place all around the outside of the holes and over the entire area of the bed. Just rip the paper to size and layer thickly, being sure to cover every bit of ground. Then wet the paper thoroughly to prevent it from flying away and so that it hugs the ground, Now, top the paper with a nice layer of soil, as thick as possible.

In the holes which you dug, place some good earth and compost or composted manure and plant your flowers and herbs. Lastly, spread a nice thick layer of mulch around your plants.

Voila! Instant flower bed or herb garden in just hours, not days or weeks.

To prepare a bed for planting next year:

Same as above, i.e., mow and outline the bed, but do not dig any planting holes. Cover the entire bed with a very thick layer of cardboard or newspaper. Wet thoroughly. Add a good layer of soil which had been enriched with compost and other organic matter. Cover with another layer of cardboard or newspaper and then top with mulch.

By next year, the paper will have composted and you'll have a nice, weed-free bed for your herbs and flowers.

There are other methods, but this is how I do it. Just three weeks ago, I prepared a whole new 40-foot bed for future planting all by myself in just a few hours. Good luck.