First, try to prevent infestations. Quackgrass spreads by rhizomes, which are thick, tough roots with nodes that can each grow into a new plant. These rhizomes spread fast and far, and can turn a single plant into a dense field. However, new plants growing from seed don't form rhizomes for two or three months, giving you a chance to pull them before they can spread. Even keeping a patch of quackgrass mown will prevent it from spreading new seeds around your garden.
Once the quackgrass is established, however, removal becomes a difficult task. The most effective methods require you to delay planting in the targeted area for one or even two seasons while you eliminate the weeds. This makes future gardens much easier to care for, and is the most highly recommended method, especially when planting perennial or woody plants that are difficult to weed around.
If you are not averse to chemicals, then glyphosate (Roundup) is probably the quickest, most effective solution. Although this herbicide will quickly kill any growing plant that it touches, most of the buds on quackgrass's long rhizomes are dormant, and so will not be killed. Applying a nitrogen fertilizer will encourage dormant buds to begin growing, allowing the herbicide to be more effective. Even with this method, the herbicide will likely need to be reapplied several times as the weeds regrow; it could take up to two growing seasons to completely eradicate it. If the quackgrass is growing among other, desirable plants, the glyphosate would have to be painted on the grass blades with a small paintbrush or cotton swab to avoid harming the other plants. Some herbicides will only harm grass (Grass-B-Gon) and will not harm most garden plants. These should also be used with caution, as they can still kill some desirable plants, such as irises, daylilies, lilies and gladiolus.
If you would rather attempt to rid yourself of quackgrass without chemicals, there are several options of varying efficacy. Again, it is best to be prepared not to plant anything in the infested location for one or two years. The plants can be smothered using several materials: opaque plastic, woven groundcovers or cardboard are often used for this purpose, and can also suppress weeds between rows in the garden. Clear plastic can be used during hot weather to solarize the soil, which kills all weeds and weed seeds after about six weeks. After this time, the bed can be planted. Organic mulches, which are sometimes recommended, are less effective in suppressing quackgrass, as the rhizomes can sometimes grow throughout the mulch. If you choose this method, be sure to mulch at least a foot deep and pile on more in any area where the grass begins to poke up.
Another method for suppressing quackgrass is to plant a green manure crop, such as buckwheat, which will successfully compete against the quackgrass for several weeks. Once it begins to flower, it should be turned into the soil and planted again so the new crop can suppress any further growth of quackgrass. The benefit of this method is that it will enrich the soil as it suppresses weed growth.
Although it takes a long time, quackgrass can successfully be eradicated by depleting its energy. No plant can live for long if it has no leaves for photosynthesis. If, for example, you rototill a bed of quackgrass, every piece of rhizome that remains in the bed will grow into a new plant. This, of course, would be a nightmare to garden in. If, however, you wait until all the grass has begun to grow (about three weeks or so) and rototill it again, and possibly up to two more times after this, the roots will eventually run out of energy reserves and they will not be able to regrow. When using this method, do not let the plants grow taller than five inches or have more than four leaves per stem, otherwise, they will begin to send out new rhizomes and you will have to start over with a worse infestation than you had before. Another method is to turn the soil over about a foot deep, bringing the soil from a foot down to the top and burying all the weed roots and seeds too deeply for them to regrow.
If you must plant in a quackgrass-infested plot, or you don't realize your peril until it's too late, frequent weeding can eventually deplete the energy of the plants. Plants that are easy to hoe between (such as corn) or that provide plenty of shade (such as squash) or that are frequently dug around (such as potatoes) will make it easier to control the grass. If any area of ground is going to be left unplanted even for a short time, some type of mulch will help to prevent weeds from colonizing that area.