Go into your garden, and measure the dimension for the area the raised flower beds. Write down your measurements, then draw a rough sketch of the shape of your yard, to scale. Draw in any landscape features, such as patios, large trees and other immovable objects, so you have an aerial overview of your "canvas," or the space you have to work with.
Consider any new design elements you want to incorporate into your garden: If you want to put in a fountain, will your red brick flower beds go around the fountain to make a circular, red brick planted border? If you are putting in a patio, will the raised beds border it? Or perhaps they will border an existing patio?
Study your landscape--a slope may warrant staggered red brick flower beds, while a dip in the landscape can be filled by stacked garden beds, forming a step-pyramid of sorts. You can also create the impression of a slope by staggering your flower beds, but remember that this will take more construction, so factor that in.
Sketch in a rough draft of where your beds will go, including any additional elements, like fountains, into the drawing. Take the drawing to the windows of your house, and check to see if the placement will be visible enough. Do this from the patio or deck as well--they are flower beds after all, so being visible is one of their main requirements; adjust the placement in the draft where necessary.
Consider the height and width of your flower beds. Factors such as soil condition, visibility and practicality (can you reach the height easily) come into play here. Also consider whether you want the garden beds to double as a seat--in this case, wide walls are essential. Mark the proposed dimensions of your beds onto a separate sheet of paper, before taking your draft design layout to your local garden center or handyman for a quote, or before buying materials if this will be a DIY project.