Raised flower beds can be as simple and cheap or as complicated and expensive as you like. All that is required for a raised bed is mounded organic materials in which plants grow. All parts of the bed should easily be accessible from outside it. A central tenet is that you never walk on it or otherwise compact the soil. Keep this in mind, and your plants should thrive.
Plan where you want your raised beds to go. This will depend on what you wish to plant and whether your flowers require full sun, partial sun or complete shade. Many flowers require full sun. If you are planning multiple raised beds, you can place one in full sun and another in shade and plant your flowers accordingly.
Stamp down any weeds or grass on your raised bed site. One of the many benefits of raised bed gardening is that it does not require digging.
Mark the edges of the areas for the beds with twine and bamboo skewers. Stab the skewers into the ground at the corners, then loop the twine around to create a border. Rectangles and squares are popular shapes, but you can create any shape you like.
Mix compost and topsoil in a 1:1 ratio. Then mix in half again as much peat moss. Mound inside your twine border until the mix is at least 8 inches deep.
Plant flower seeds, bulbs or transplants. Mulch around the plants with shredded newspapers and cardboard. Top that with grass clippings from your lawn as well as dried leaves (if you have them). Mulch should add about 3 inches to the top of the soil. Do not pile mulch directly next to plants, or you run the risk rot.
Turn the soil and mulch over when the growing season is done, if you have planted annual flowers. Do not turn over perennials. Turning the organic matter into the soil speeds the breakdown process, providing rich organic matter and nutrients to all future plants in those beds.