Answer: Lucky you with a new garden spot! Grass can be a real problem for new garden beds. Under certain conditions it can sprout and create a nasty weed problem. You mention double digging which is a technique more commonly used in the UK than in the US. Double digging involves the removal of about a foot of topsoil in order to loosen, aerate, and amend the subsoil beneath it. The topsoil is amended and replaced systematically in a trenching process that takes considerable time and effort.
Because of the effort put into double digging, perennial weeds including grass, are usually removed. This can be done by several methods including cultivating with a roto-tiller or using a contact herbicide which you mentioned, or you can completely remove the sod with a sod-lifter. Each method has its appeal; the important point is to be sure the grass will not regrow.
Killing the grass with a weed killer insures it will not be a problem, but many gardeners do not like using chemicals on their soil.
If you cultivate, don't make the mistake I did when I started my first garden, and only made a few passes, not very deep. I fought grass all summer long in that garden! Some grasses are pretty resilient and need to be shredded to insure they will not come back. On the other hand, some weeds, like purslane, can regrow from the tiniest piece if they receive light and moisture, and should be removed or buried deep to insure it will not come back. You need to know what you are dealing with in the area.
Lastly, totally removing the sod is not a method I would recommend if avoidable. While it seems like the perfect solution to remove all the grass and roots, you will also be loosing the top 2 inches of soil, which would be a real loss to your garden. Even then you would not be assured it would be weed-free, since likely there are seeds below waiting to germinate! If you should choose the sod-lifting method, be sure to save the grassy sod for the compost pile, so it will not be wasted.
Here in the US most gardeners do not take the time to double-dig their own gardens because of the time and effort it takes. In my own garden, to insure success without becoming discouraged, I would first start small: better to successfully tackle a small area, then to have a large area with only mixed results. It's too easy to become overwhelmed! After limiting my garden area, I would cover it with black plastic or heavy layers of paper (held down by rocks or sod) to keep the light out and kill the grass. Several weeks later I would roto-till very well, making repeated passes. On the final several passes I would add compost or other organic matter to the soil. Then I would continue to amend the areas as I placed each plant or seeds. Each season I add extra amendments in the form of mulch or compost. While this is not as thorough as the double-digging method, it is one that works well for my time and gardening style. Another tip: if possible, plant annuals rather than perennials for a year or two so you have the opportunity to completely roto-till again adding more amendments. Hope this gives you some options and answers. Enjoy your new garden!
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