Say, I would consider removing that upper layer of cardboard, the one you just added after adding soil. All that great cardboard on the bottom will be awesome as the base of your bed, but layering it in middle laters probably would hinder the mixing of your growing medium and make it harder for fall crops to send down roots. You could mix up the soil and the grass clippings as you go up.

Perhaps, you should tear up that last layer of cardboard to speed decomposition.

Do you have drainage holes or is the concrete sided bed on top of soil? Be careful about adding garden dirt because it doesn't drain as well. Thin layers of vegetative material such as grass clippings will decompose and if you have thinner layers you won't be creating a hot compost pile... Then you can plant your fall crop. If you have compost that would work for little pockets where you plant your plants.

Other ingredients:
composted manures - it still smelly they're hot & can't touch plants, so on bottom layers
used coffee grounds
shredded vegetation clippings (leaves & stems) without weed seeds (mower does a great job of it)
shredded kitchen scraps - as your meal is prepared you can blend in a blender for dumping as a layer as you go
spoiled alfalfa hay or feed store sweepings - great bottom layers & don't cause a weed problem

Hope that helps~

The "dirt "I added was just from elsewhere on my property and doesn't look very good at all. Its very light brown, almost white, very slippery when wet, doesn't drain well, and stinks. I probably should not have put it in, but I wanted to throw something in there other than just cardboard. It does support the vigorous growth of weeds, so I guess it can't be all bad, but it doesn't look anything like the black stuff I have in my other bed that I made out of grass clippings, shredded paper, and some store bought top soil. It is a little sandy, so I hope that once the cardboard decomposes, mixing all this together will give me something worth while. If not, I guess I'll have to resort to urinating on it.

Only on the compost forum do you end a post with "If not, I guess I'll have to resort to urinating on it." and it sounds perfectly reasonable.

Lol. Yeah that and "other" websites. But I agree with this entire thread. The more the merrier

Yep, still trying to train our dog to pee on the pile instead of the plants...