There is no magic cure to make weeds go away. Weeding is part of maintaining a garden, and the more regularly and consistently you weed, the easier and quicker it actually is.
Weeding is removing unwanted plants from the ones you want to be productive or ornamental in your garden. You decide what a weed is. If a tomato sprouts in the compost you spread around your roses, you will probably pull that tomato out, even though you grow tomatoes in your vegetable garden. Don't be afraid to remove a "good" plant if it's not where you want it. You want the plants that remain to attain their full growth and maturity, and weeds steal sunlight, moisture, and other resources from the plants you are intending to grow.
The best time to weed is when the soil is moist and the weeds are very small, mere seedlings. If you make weeding part of your daily stroll through the garden, you can spot and remove them as you monitor for pests and harvest crops.
The best tool for weeding is your hand. There are situations, however, where something more is called for. If you have many small seedlings, a hoe (either long- or short-handled, like a Ken-ho weeder) can cut them all off at soil level with a few swipes. If you discover a tap-rooted weed that's attained some size, a Hori-hori knife will help you prize it out of the earth.
The best way to prevent weeds is to leave no bare earth. Space plants close together so they shade the ground between them, and mulch the soil. Most weed seeds need light to germinate, so these two practices go a long way to minimize weeds. Also avoid disturbing the soil when possible, as this brings new weed seeds to the surface where they can germinate.
Work especially hard to remove the roots of perennial weeds, as they will often resprout from root pieces left behind. Above all, don't let any weeds go to seed, as that will only increase your weeding next year.
Weeds seem harmless when they are small, but that is when they are most easily defeated. A good rain followed by a hot spell means a sudden growth spurt for the weeds, and suddenly a task of a few minutes becomes a big chore that you put off. Remove weeds when they are small, daily if you can, and weeding will be no big deal.