First, decide what plants you would like to grow and the amount of space you will need. Consider the region you are in, the space available, and monetary investment. Google is good for gathering information, as well as your local Extension Office for answering any questions you may have. Once you've decided, purchase the necessary Rubbermaid containers. Luckily, there are plenty of color and size choices out there. Do remember to try and avoid see-through containers though, as algae can grow there.
Second, prepare your containers. Drill 3/4" holes in the bottom and around the bottom sides of the container. You can use the lid, placed up-side-down, as a good drainage catcher, but make sure you have something to lift the container up off the lid so that air can get underneath, and so that the excess water will actually drain. I used deck banisters cut in half. I used a few pieces per container, placed them on top of the up-side-down lid, and then placed the containers on top of that. I was also mindful of where the drilled holes were in relation to the banisters and tried to make sure that none of the holes were blocked.
Third, start filling. I used marble chips in the bottom of the container to fill up some space, and also to allow for more draining. They are relatively inexpensive, and cheaper than the potting soil, so I filled them up about 1/3 of the way. Next, I used Miracle Gro Potting Mix. I filled up the container the majority of the way to the top (roughly 3-4 inches from the top) with the potting soil. If you are growing tomatoes, you should also mix in some peat moss. This will aid in the acidity of the soil, and will also make it light and fluffy.
Fourth, start planting. At this point, you are ready to plant. Make sure you provide each plant with enough space to grow, and support where needed. Tomato cages are a wonderful thing, as well as trellises. What kind of support you will will depend on what you are planting. To plant, I create a small valley with my fist... wide enough to allow the plant to go down, and deep enough to go to the base of the plant. You will want to make sure that the top of the soil in the plant pot is below the level of the soil. Crush roots very gently, place into the hole, and then cover with soil. Make sure none of the leaves are touching the soil - this promotes disease. And if they are, feel free to pinch them off.
After I finished planting, I added a layer of mulch on top of the soil. This helps retain water and also protects the soil... and it also looks good. :)
And there you have a container garden.
Remember to water well and watch them closely.
Oh, and talk to your plants - it makes them happy!