Are you talking about garlic mustard? If so, it reseeds freely and the seeds can remain viable for years. It required diligence to get rid of it; you must pull up every single plant before it goes to seed and remove the plants from the area (bag them and throw them out; it's not a good idea to compost highly invasive plants).

What I have done in areas heavily infested with perennial weeds is to prepare my soil, plant what I want, and then lay down layers of wet newspaper (about 6 layers deep will do it) and mulch directly over the wet paper. This gives the weeds very little to root in (though things like crabgrass will start to grow right in the mulch).

If you have exposed top soil, annual weeds will grow right in it. Several inches of mulch will minimize that problem, but not stop the perennial weeds. That's why we use the paper.

Garlic mustard is a biennial, btw. The first year rosettes winter over and the second year they send up flowers (April or May where I live) which reseed heavily. Pull it out now before it goes to seed, but it will take several years to exhaust the seed bed.

A stirrup hoe can be used in areas where the plants like vegetables are grown in a line. It has a hoop in the shape of a square or circle. The hoe cuts the seedlings and can also uproot them. This helps in ensuring that the weeds do not emerge again. But in places where the weeds are growing quite close to the main plants, you need to remove them by hand as there is a chance of damage by the hoe.

Mulch is also effective in reducing weed growth. It works by preventing the sunlight from reaching the soil thus inhibiting any growth of weeds. Clippings of grass, branches, hay and other degradable substances like leaves and barks can be used.

Here is a link that might be useful: Organic Weed Control