Often the easiest and most effective way to control weeds is to simply pull them out by the root and dispose of them.
Getting to know the weeds
The first step in removing weeds from a garden is knowing which plants are weeds, and which are not. Inexperienced gardeners should always have an identification guide handy to help with this, or use on-line resources such as the Bloom Clock on Wikiversity. Once identified, further reading will let the gardener know what kind of root system the weeds have, how they set seed, and whether they are safe to compost.
Once the weeds are identified, the gardener should start pulling them out. If soil consitions are not conducive to getting the full root out (e.g., too dry or frozen), it's generally better to either change the conditions first (e.g., by watering) or just coming back another time, since most weeds will regrow from the root if only the tops are removed.
Many weeds will simply break off at the ground if pulled using a quick, jerking motion, so pull slowly but firmly to ease the whole plant out of the ground. If a root will not come out, either use a tool such as a hand cultivator or mattock to grub it out, or for large weeds (particularly woody ones), just cut it below ground level using loppers.
Dispose of quickly and properly
Never leave weeds in piles, either in the garden bed or on an adjacent lawn or other surface, since in many cases the seeds will continue to mature and disperse even after the weeds have been pulled. Most weeds can be composted, though if seeds are present heat composting may be required. Some weeds should simply be burned or sent to the landfill if they are particularly invasive.