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.
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!
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Edited to add:
I would recommend this form of gardening for your non-food-bearing plants.
The discussion regarding the release of toxins from the plastic containers into the soil and thereby the food is an interesting one that would require more research. And if you have insight, please feel free to share in the comments!
But all in all, still a great option for a garden!