The fleece (also called floating row cover) is secured to the ground with rocks, landscape staples, or heavy garden stakes. It's placed over a frame such as a wire cage on its side. If the leaves of the plant touch the row cover, they may get damaged. It may protect plants from a frost that lasts only a few hours; I don't think it works for a prolonged frost. The advantage of using floating row cover (vs. sheets or blankets) is that it lets water through and transmits light, so it can be left on until it's warm enough to leave it off entirely. If you used boxes or blankets, you'd have to cover the plants in the evening and then take them off in the morning, every day that frost was forecast.
When I've planted tomatoes early, I've used walls-o-water -- a plastic cylinder that surrounds the tomato plant, with tubes that you fill with water. It can be angled over the plant like a tepee for more protection, or placed with the sides vertically. It's like a small greenhouse for the plant. In my clilmate, I need to protect tomatoes from windy days and nights usually around 45F, so I leave the walls-o-water until mid to late May. They keep the plants warmer at night. When the plants grow over the top of the water walls, I wrap the tomato cages with bubblewrap, or at least cover the top of the cage so that morning dew does not fall on the foliage.
Flaoting row cover is also used to keep pests off of plants, such as cucumber beetles. The row cover is removed only when the plants begin to bloom, so that they can be pollinated.