I have been a fair weather gardener for a lot of years. Just last year I decided to become a more avid gardener. It was worth it. I think I have found a way to get the grass out once and for all without chemicals or vinegar. Now I will be able to enjoy my garden.
I tried spraying vinegar it works okay. It works great if you heat it up first so it burns the plant a few different ways. I found this to be more expensive than round up. It only worked if I drenched the plant or sprayed multiple times. It took a lot of vinegar and at almost 5 dollars a gallon was very pricey. Since I could get the same amount of round up for just a few dollars more and use half as much to get the same results. I went with round up for a while. It still would not kill the grass all the way and had to be sprayed more than once. Also once my garden was planted it didn't help me since I couldn't spray close to the plants without killing them to.
Then in August last year I found a great solution. I never expected it to work so well. I have a border around my garden of just bare dirt to try and keep the grass at bay; or it was suppose to be bare dirt but a lot of grass had filled it in. I dug up the grass in that area and just flipped it over. I then chopped the clod with the side of the shovel to even the ground out again. It worked so well that even now there is no grass growing in that place. I then winterized part of my garden that way in the fall just before the freezing temperatures set in. I am very pleased with the results so far but it didn't work as well as the one I did in the heat of summer. It still is a lot better than if I had done nothing at all since I know what that looks like based on the other parts of my garden I didn't get done.
Now it is simple to just dig each square (4'x4') and flip the grass that is growing or take out the grass by the roots. I have the awful grass that sends out multiple runners and keeps popping up in unexpected places.
I think it worked because it confused the plants since the roots are in the air as well as the heat drying them out. Also since it was in a walk way I first did this, which has a high volume of foot traffic, it made it too difficult for the grass to recover.