Once you have the right plant, the right pot, and some premium quality potting mix like Miracle-Gro® Potting Mix (don't use garden soil!), it's time to put them all together.
Filling and Planting Your Pot
Before filling your pot, cover the drainage hole(s) at the bottom with a coffee filter, piece of screening, or scrap of landscape fabric. This will keep soil from spilling out of the hole but still let water drain; don't use anything that will stop drainage. If you have a heavy pot, consider putting it on casters for easy movement. Then fill the pot with potting mix, to an inch or two from the rim of the pot. Plant your plants, then fill in around them with more potting mix, if needed, to be sure that the roots are properly covered.
Don't press down and pack the potting mix, though you may want to tap the pot on the ground or rock it back and forth a couple of times to settle the soil into air pockets. Water gently, allowing the water to drain through the pot, wetting the potting mix as it goes. Water a second and a third time to be sure the soil is thoroughly moist. Excess water should be draining from the bottom of the pot. For a quick nutritional boost, add liquid plant food (like Miracle-Gro® LiquaFeed® Tomato, Fruits & Vegetables Plant Food) to the water. After you're done watering, take a look at your plants to be sure that their roots are not exposed or planted too deeply (unless it is a tomato, which requires deeper planting).
Finally, add a layer of mulch on top of the potting mix to help conserve moisture. Good mulch choices include wheat straw, pine straw, and soil conditioner.
Watering
Your potted vegetables will need plenty of water as they grow. You will know it is time to water when the top inch of potting mix is dry to the touch. You will also learn which plants dry out the fastest. Once plant roots have filled their pots and the weather gets hot in summer, you can plan on watering on a daily basis. Remember that fluctuations in soil moisture can worsen blossom-end rot in tomatoes. It is better to have constant moisture than to alternate wet and dry conditions. Consider a spaghetti tube drip irrigation system if you have a lot of pots clustered in a single place that is easy to run water to. It will make watering a breeze.
If you are growing vegetables in pots during the winter in an area in which temperatures could freeze the soil, your plants may wilt because the moisture in the soil is unavailable to the roots. If you have a sunny south- or west-facing wall, that is a good place to put your pots and grow your vegetables. Masonry is particularly helpful in creating a beneficial microclimate, releasing the warmth of the sun to prevent cold damage at night. See Keeping Pots Watered for more about watering.
Fertilizing Your Pots
If you are growing vegetables that produce fruit, such as tomatoes, peppers, and squash, avoid fertilizing with too much nitrogen. Nitrogen (the first number in a three-number fertilizer formula, such as 10-10-10) encourages leafy growth at the expense of flowering. For example, you may have a beautiful tomato plant, but few fruit. However, if you are growing lettuce, basil, or another plant whose leaves are your goal, nitrogen will fuel production.
In either case, you'll want to fertilize regularly and moderately. Some potting mixes have a short-term supply of fertilizer in them, while others are slow-release over a long period of time, so be sure to read the label. If you are using short-term fertilizer, don't add additional doses for the first 2 to 4 weeks, depending on how often you have to water.
The frequent watering required by container plants will wash away nutrients more rapidly than if the plants were grown in the ground. Help replace them by using a continuous-release granular fertilizer like Miracle-Gro® Shake ‘n Feed® Tomato, Fruit & Vegetable Plant Food, or a plant food that you mix with water, like Miracle-Gro® LiquaFeed® Tomato, Fruits & Vegetables Plant Food. (Either way, be sure to follow the directions on the label.)