For the canvas models: You really don't. Although they should be secured using tent stakes, as they are light and can be carried away by the wind.
For solid wood: It depends on the model. The simple patio gazebos can sit on the ground with no ill effect, but the much heavier octagonal and studio models need a firm foundation, as with any building. Otherwise they can sink into the dirt after a good hard rain, making your beautiful gazebo unlevel.