You can dig them up with a small trowel. You can then put down some newspaper and put down mulch to prevent future weeds.
This video tutorial is helpful:
Unfortunately, if you have plants you want to keep in your garden there's nothing you can put on it that would only kill the weeds. Lauren of Mom Home Guide had the vest solution. Pull and find a way to mulch. Use cardboard, grass clippings, newspaper or straw. If it's a flower garden put 4" of mulch everywhere, even around the base of the plants
Hi Elizabeth: Here's what I use, and it works only on what you spray it on:) If the weeds aren't over about 4 inches tall, you can make a mix of:
1 gallon of white vinegar
2 cups of Epsom salts
1/4 cup of dish washing detergent, like Dawn.
Mix the vinegar and salt until the salt is dissolved, mix in the Dawn until mixed well, but not all fuzzy and sudsy.
Put in a sprayer and spray the weeds liberally, in the morning after the dew has gone. Then, by evening the weeds should be dead or on their way out. Don't spray anything you want to keep or it will die too. I have done this and it works. Also, it's good for making an edging as it kills only what it touches. If you have something like a piece of cardboard, hold it up and down, edgewise, and spray the area you want as an edge. Just be careful not to spray your flowers and/or bushes. Good luck