We've shared this tip before in Washington Gardener Magazine, but I thought it was worth repeating here for any newbie gardeners:
Vinegar is a safe, cheap, and easy weed-killer. This works best on a sunny, not windy day. Spraying with vinegar (full strength from the hardware/cleaning supply stores, not the grocery store kind) with a dash of dish soap added for "clinge." Spray on in the morning and let the sun "fry" the weeds all day. Wait a few days for full die-back and then pull them. This is so helpful in border places like on a fence line and along pavement cracks where weeding tools just cannot reach to get all the roots out.