Weeds, quite simply, are plants that grow where you don't want them to--like dandelions in the strawberry patch or crabgrass in the front lawn. Weeding plants only works if you keep in mind one thing: You need to remove the root. Otherwise, the weed will grow back. There also are several preventive steps you can take to make sure weeds don't come back.
Cut off any flowers or seed pods before you begin, so the motion of you removing the weed doesn't trigger an avalanche of seeds into the soil. This is an especially critical first step in weeding your garden of milk weeds or dandelions.
Loosen the soil around the weeds with a fork, being careful not to harm the plant you're trying to protect. You also can pull out sections of weed with the fork, although you generally won't get the full root unless you are going after a surface weed like crabgrass.
Put on your garden gloves and with the thumb and index finger on your right hand grab a weed as far down as you can get. Make sure you get the top of the root, just below the ground line.
Give the weed a firm tug, and then slowly pull the root out, pulling straight toward you. If you meet resistance, don't force it or the root might break. Instead, dig deeper with your fork to expose more root.
Use your shovel to completely dig out the root of really stubborn weeds with long roots.
Lay a patch of carpet around the plant after you've finished weeding so an errant portion of the weed's root you might not have been able to remove doesn't have the chance to grow back. Depriving it of light is the best course of action.