Choose an area near an entrance, an area where people congregate, or a sidewalk or seating area. These areas are where people will be, and you'll want your flower garden to be visible. Don't put it in a traffic path where it will have to fight for survival, however; find a space just to the side of one of these busier places.
Mark out the small flower garden with rope or a garden hose, then step back and look at it from the direction in which most people will approach. What do you notice? What is in the background that might be distracting? Are there large trees or bushes that overwhelm the area? Make a note of what surrounds the flower garden and what might need to change.
Clear out as much as you can just around the flower garden so that it's not covered up by larger plants. Prune trees and trim shrubs back so they aren't edging in on the flower territory. Clear out any weeds, debris, trash, or outdoor gear such as trash cans, hoses, or wheelbarrows that will distract people's focus from the flower garden.
Till up the area for the flower garden (remove your hose or rope that marks it first!), then spread a three-inch layer of organic compost or well-dried manure on the area and till it in to the soil. A garden tiller usually works the soil to about 12 or 18 inches, and that's deep enough to prepare the soil well for the flowers that will be growing there.
Create an edging of some kind. Edgings serve four purposes: they designate a space, they contain plants inside the space, they keep weeds and grass outside of the space, and they enhance the appearance of the plants. The edging material you use tends to set the tone for the flower garden. You can use a plastic landscape edging that simply sinks into the ground and isn't really seen; it will help contain plants and keep grass out. Or you can use a row of stones, bricks, landscaping stones, river rocks, or logs. It's very much a matter of preference.
Pick a color scheme and stick to it. A small flower garden has more impact if it greets you with a bold splash of a single dominant color rather than a lot of hues crammed into one space. Too many colors creates visual confusion. Pick one color to be your main color: blue, orange, pink, red, purple, white. Choose what you like. Then purchase most of your flowers in that color family, and add a few in an single accent or complementary color for just enough visual interest.
Work in three levels when you start adding plants: ground level is the first; waist high is the second; and eye-high and above is the third. Place your tallest plants at the back of the garden, your waist high plants toward the front, and your ground level plants around the edges and as ground cover between the taller plants in the back.