As above, no miracle cures in the case of Alliaria petiolata.
Begin by pulling it or applying an herbicide to it. (First-year, non-blooming plants can be pulled or treated with herbicide but second year, blooming plants should be pulled as they may still set seed even as the herbicide kills them.). Patches that are in their first year and not extensive might be killed under a smothering layer of paper and mulch.
(We wrote about this in our newsletter, too: At GardenAtoZ.org, go to What's Coming Up 177, Confident Weeds.)
Areas you've cleared must then be mulched well and/or covered with a layer of some other very-fast sprouting, dense growing plant so garlic mustard seed in that spot can't germinate. Pre-emergent herbicides can help prevent new invasions by seed. However, keep in mind that garlic mustard seed will sprout almost any time so a single application in spring, as for crab grass, is insufficient against this pest.
If garlic mustard is relatively new in your yard, do what you can to locate and control the seed source. Often, it's an established infestation upwind or uphill that's sending its seed your way.
Persistence is key. Where we are battling garlic mustard we are perpetually on patrol. We reach down and pull the plants even if we're just walking by to gather a forgotten tool.