Decide what you want to plant. For my example we are going to use lettuce.
Purchase the seeds or plants, soil, and container for planting.
Choose the seed you want. There are various seed companies where you can purchase seeds. Home Depot, Lowe's, Wal-Mart, Co-Op, Mayo's, Tractor Supply, etc. also have garden seeds and most places sell organic seeds as well. You can also purchase lettuce plants this time of year as well. If you decide on a plant, then you will be able to enjoy your planting much earlier than from seed.
Purchase soil. I suggest getting an organic potting soil mix. An example is Miracle-Gro® Organic Choice® Potting Mix . You can get this potting soil at Wal-Mart, Home Depot, Lowe's, etc. This Potting soil is designed specifically for container planting. If you have a compost pile or some other nice soil around your home, you can use that as well and save money.
Choose the container. There are various sizes of containers. You can even make your own, The most important thing is to make sure there are drainage holes int he bottom. Also, if you plan on keeping your container in doors or on the porch, you will want to make sure there is something under the container to collect the water which will be draining out of the container. If you do not have the money to purchase a nice container, you can use a plastic tote or some other type of container. You can use a small drill to drill drainage holes in the bottom or make some with a knife.
Now that you have all of your materials, you are ready to begin planting.
If your soil is dry, you should lightly moisten the soil before planting. If you are using seeds, make sure the soil is warm as seeds will germinate best in warm soil. Fill the container to the top if you are planting from seed. Leave about an inch space if you are using plants. For seed check the depth the seeds should be planted. In our example, lettuce is not planted very deeply. You can actually just sprinkle some seeds on top of the soil and lightly cover them with soil. For plants you will want to evenly space your plants around the container, but you do not want to put too many plants in your container as the soil will not support a mass amount. . Make a hole in the soil and place the plant. The hole should be about the same same depth and about 1 1/2 times the width of the plant. You want to cover the roots and try to keep as much of its original soil attached to help avoid shock. Add more soil in order to fill your container to the top. After planting you will want to thoroughly water your soil. You may or may not need to water every day. You can touch the soil with your fingers and see if it is wet. For lettuce, you will want to keep the soil moist, but not overly wet. Too much water or too little water will not yield good results.
Wait. Pick. Eat. Enjoy!
Your seed packet or tag in the plant pack should tell when you can harvest.
Good luck. I did not go into a lot of detail. Let me know if you have any questions. I would love to see pictures especially from those of you who have never done any planting or gardening.