It really depends on the kind of
weeds and their location. Anything with a taproot needs to be pulled, unless you're prepared to cover it with a rock for a whole season. Vines need to be dug out. I've got a trumpet vine that even Round Up can't stop. But for run-of-the-mill annual types, boiling water, vinegar, and covering them work pretty well.
Paul Jones, the gardening guy on HGTV said 20% strength vinegar would kill
weeds. But the vinegar you buy in the store is only 5% and I haven't yet found a place to buy 20% dilution. So, I just sprayed household vinegar on various
weeds in the cracks of my driveway. It killed some. I wouldn't do this in a garden, though, because vinegar will change the pH of the soil.
I've had some luck by pouring boiling water with salt dissolved in it over
weeds. That will kill just about anything
growing in cracks, but if you're looking to kill
weeds along a fenceline for example, I wouldn't put all that salt into the ground for the same reasons as vinegar - it'll change the pH. I was amazed at how much boiling water it takes and how complicated that can get running from the kitchen to the
weed patch with pan after pan of boiling water. Just "hot" won't do. I've had the idea to use one of those steam sprayers, but haven't tried it yet.
You can also kill
weeds by covering them with black plastic or thick newspaper covered in mulch or dirt. Even an old sheet of plywood will work, if you don't mind how ugly that is. You've got to leave them covered for at least a few weeks to weaken them enough that they're easy to pull by hand. Leave them covered for a whole season to kill them without having to do much else, but realize that any
seeds that were on the
plants will probably germinate once they're exposed to sun and moisture. But they should be easy to keep up with by hand from there on out. Till and
plant something you want before the "weedlings" have a chance to take over again.
With the woodier varieties of
weeds, i.e. bushes and sprouting
tree stumps, I've had some success pounding a penny into the meatiest part. It sounds a little nutty, but I'd read many years ago that copper in large enough amounts being absorbed into a
plant will kill it. Not having any copper nails on hand, I made slits with an ax and then pounded in some pennies. It worked! Just remember to remove the pennies before you put that stump into the chipper.