It will take years to get this problem under control now as all the weed seeds will sprout again as soon as you remove the present weeds. All I can suggest is hard work and persistence.

What about using corn gluten meal as a pre-emergent?

What - besides weeds - is in the beds now? If currently empty, cut the weeds back, cover with cardboard or several layers of newspaper, then a layer of the mulch of your choice, thick enough to hold down the carboard/paper through winter and any winds. By spring, the weeds should have pretty much died off and the whole works can be worked into your soil in time for new plantings. There may still be a few perennial or deep rooted weeds present but removal at that time should be relatively easy.

If the beds are planted, you can do much the same thing in between the plants (unless too dense). Be sure to clear the area directly around the base of the plants of any weeds and then cover with mulch, avoiding piling any mulch directly against the base of the plant.

The other option is to bite the bullet and manually remove as many weeds as you can, then mulch to cover soil and retard regrowth. A decent layer of mulch is really very effective in controlling weed development and depending on type, will only improve current soil conditions. And be sure and apply mulch next season after planting to prevent this situation from developing again. Weeds can be a problem for any gardener so be sure to stay on top of them.

Yes, flattened corrugated cardboard boxes will take care of the problem. Wet them down and cover the entire bed. You do need to cover with something else as gardengal has said to keep them from blowing away. When I have access to hay or straw, I use that. In an urban setting if your municipality collects lawn waste and yard detritus, you can probably get ground up tree limbs for low cost to use. Where I live they don't do that so I buy cedar or pine bark mulch and use that.

If you go the bark mulch route that won't rot into the soil anytime soon but it is easy to pull it back and replace or remove last year's cardboard if that is your choice. I treat this as permanent mulch and add cardboard every couple of years as it breaks down. I can cut through the cardboard with a box knife to plant through the cardboard. I do not otherwise disturb my soil once I have it set up. Cut a hole large enough that it will leave a space for watering the plant. I use drip irrigation or hand water.

As I am in an area untroubled by slugs, I do mulch all the way up to the plant base. I have in fact done this pretty much everywhere I've ever lived and slugs are not usually a problem. If you are in a slug-rich environment - say, Portland, OR - you will definitely want to keep the mulch AND the cardboard weed block away from your plants.

This method of mulching my garden plants is so effective and so easy on the water bill that I am willing to pick slugs every morning if I have to. I've only been in that situation once in decades but the garden was so small it really wasn't a problem. However if I ever have to deal with slugs again, I'm likely to start relying on Slug-go.

Even if you don't choose to continue to use the cardboard (covered by mulch) as weed block, this will definitely kill off your weeds and many of the weed seeds as well. If you want to do a soil sterilization to kill even more weed seeds, in the spring, pull off the cardboard and all mulch and cover with CLEAR, not black, plastic. It needs to be in soil contact not suspended over the bed by draping it across the bed walls. Weight the edges down with scrap lumber or anything else heavy enough to keep it down. Clear plastic will heat the soil up even more than black plastic. This will kill weed seeds for about 6" deep. It won't kill your earthworms, they will just retreat deeper in the soil.

If you don't want to mulch forever, don't use hay. It is nearly always full of weed seeds. This is not a problem as long as you keep mulching (especially with the cardboard underlayment as weed blocker), but the results will be less than salubrious should you ever stop.

I like cardboard + mulch. I never have to disturb my garden soil except right where I'm planting and everything thrives.

Please don't use Roundup if you are going to grow veggies there. I don't spray any chemicals near my food crop area. Clear plastic during the hottest months for 3 months next year should help. If you can grow your veggies someplace else. Not sure about quack grass. The plastic has to be secured tightly to the ground to prevent any water or dampness getting in.

My method is to water and wait for germinations of weeds, then remove all weeds before they go to seed and do it again and again. Eventually all the seeds will sprout and new seeds will stop being made, and naturally I add a mulch of woody type to soften the soil and make the weeds easier to remove.

Cardboard, plastic, any "weed" barrier will not stop Quack Grass, nor will the glyphosate sprays. The only method of control that works with Quack Grass is to dig the rhizomes
(roots) out. Tilling where Quack Grass is growing appears to suppress it for a while but those rhizomes will sprout even more plants, although tilling can bring some of them to the surface where they can be pulled out.
A field Rye cover crop can help slow the growth of Quack Grass some, and in my experience, black Walnut leaves can also suppress its growth for a while. A cover of clear plastic will simply encourage the Quack Grass to grow faster, I have seen that stuff pushing clear plastic up and out of the way if not punching holes in it.
If you cannot dig into these beds your self you may need to think of hiring someone to do that for you.

Thanks, all.

Zackey, the reason roundup is not attractive to me is that I've tried to eliminate chemical use. I can't claim to be organic because I'm not always careful what fertilizer I use, and once in a fit of frustration I painted sevin on the stems of my summer squash to kill SVB. I do try, however, not to use the nasty stuff.

For those who've recommended solarization, I considered that option in depth but wound up dismissing it because of my zone and the cooler summers we've had. My garden is in between two one-story buildings (my house and my garage) and is east/west facing by necessity. It does get several hours of sun, but I'm not confident that it would be enough to kill stuff very far down, given that the hottest air temps rarely exceed 85-90. My local extension does not recommend it due to those reasons, and because it's not reliable for rhizome grasses like quackgrass. Do you all think that solarization could be effective? I'd try it if I thought it would work.

Gardengal and Zensojourner, I like the thought of cardboard under mulch - one or the other alone, I don't think would be enough, but both together is an attractive option over black plastic. four years ago, I started the beds with cardboard between the soil of the bed and the ground underneath it, and it did block the quackgrass for about a year. How would you plant things, like carrots or potatoes, in the cardboard, things that you can't start as transplants first? Just cut a strip or hole out? And fertilizers - remove the cardboard to apply, right?

You've got some great suggestions above to consider.
Here's my 2 cents to add (and I have won the West Virginia State Quack Grass Digging championship for 8 years running.)

I think your best option may be cutting the tops of the weeds off now (fewer seeds to fall) and using the cardboard plus heavy mulch idea. (But skip the black plastic -- let the soil breathe a bit. I've seen nasty mold growing under that stuff.)

Then in spring I think you'll have to pull the much off and dig your quack grass rhizomes out -- but this should be relatively easy because the soil will be soft, and the rest of the weeds should be gone.

Once you get the QG under control, on a future year if the weeds take over, I think solarization could work in your area. Solarization seems to me to be more a matter of height of the sun than heat. We never get to 90, and rarely get to 80, and the year I put the plastic down in late April it worked way better than the year I put it down in early July (and the "heat" if you can call it that, doesn't get here until August). (each time I left it on for a couple months)

So, solarization in the early spring until you see dead underneath could be worth a try. And remember to WET the area thoroughly first -- that's part of solarization, for whatever reason. But, as has been mentioned, this won't help you with the quack grass.

No lecture coming from this gardener. I "lose control" of a bed or two (or three!) every year, and have to go back to square one with the quack grass and weeds. I think of quack grass digging and an opportunity for mindfulness. Once the quack grass is gone, I'll be enlightened :)

Cardboard or newspaper products should be fully decomposed by the time spring planting rolls around. And if you use a compost or manure type mulch over the top of the paper product, then all you need to do is work the layers lightly into the soil, remove any persistant weed remains, rake smooth and plant. For a woodier based mulch, just rake it off to the side, follow the above steps and respread the mulch after planting.

Yes, the best way to use cardboard is to sacrifice a portion of the growing season, wait till weeds have sprouted, then smother them. Assuming you do this in June, you can punch holes in the cardboard/chips and plant cabbage, chard, or other medium/large veggie with a short season. It will make it by the Fall. Smothering now will not work.