Lay down a landscaping membrane. This works to suppress weeds by shielding the area underneath from the air and sun. Openings must be made for flowers and vegetables, along with slits for shrubs and trees.
Spreading a mulch (like bark chippings) around the base of plants also helps to prevent the growth of weeds. It works much in the same way as membrane by limiting the amount of air and sun. It can also add a pleasing aesthetic feature to your garden with the use of materials such as attractive stones.
By combing the use of both membrane and mulch, you will have particularly effective weed prevention.
Herbicides can be of use in areas such as pavement cracks and in established areas where a membrane or mulch cannot be laid down.