Planting a container garden couldn't be easier. All you need is potting soil, plants, and slow release fertilizer. That said, there are some things it's helpful to know before you start.
Make sure your container has enough drainage - Drainage may be the single biggest factor on whether your plants live or die. Make sure that your pot or container has a big enough hole or holes in the bottom to let excess water drain away.
There are many pots sold in stores that have one tiny hole in the bottom that will not let enough water escape. If you decide to buy one of these pots, you will either have to be very careful watering, or even better, you should add more holes. If your pot is metal, chances are that you can poke holes by using a hammer with either an awl, large nail or the end of a screw driver. If your pot is ceramic, it can be a little more difficult to add holes, but I've had good luck using a drill with a ceramic bit (don't forget to wear safety goggles, because it is common for pieces of the pot or dust to fly around and you don't want to risk getting them in your eyes). Remember--the more holes and drainage the better. Many more plants are killed by drowning than not enough water--though I have done my share plant murder by both.
They second part of the drainage equation is keeping the soil in while letting the water out.
I like to use plastic window screening over large holes, but I have also used coffee filters, paper towel, newspaper and fancy products, like Better Than Rocks in the bottom of my pots and they all work.
Whatever you do though, avoid the suggestion to put gravel in the bottom of your pots to increase drainage.
It doesn't work, and in fact it is counter-productive.
It is also a good idea to elevate your pots, so that the water isn't blocked from exiting out of the drainage holes. There are any number of ways to elevate your plants, but pot feet are the easiest.
Pot Feet Rock
More on Watering your Plants
Choosing a Container
Tips for Unusual Containers
Remove your plants from their nursery pots carefully - When I first started gardening, I would grab a plant by by the stem and give it a tug to get it out of its pot. Often I would just pull the top of the plant off sometimes killing it before I even got started. To avoid this, if you have a six pack of plants made of flexible plastic, hold the plant close to the soil surface (I make a v out of my fingers and place them on either side of the stem) and squeeze the plants out of their holder from the bottom. If the plant is in a nursery pot, try pushing it out from the bottom. If it is root bound, you may have tear or cut any roots off that are sticking out the bottom hole of the pot and slide a knife around the inside of the pot, before the plant will slide out.
In extreme cases, you may have to break the pot to free the plant.
If your plant is root bound, which is often the case, make sure to break up the roots, either by tearing them or cutting them. Some people simply rough up the roots on the outside by rubbing them, but I'm a little more aggressive and often tear or cut a compacted root ball so the roots will be able to grow freely, not in a circular pattern, which can strangle a plant.
Mix fertilizer into your soil - It took me years to realize that I was starving my plants to death. Most plants need food to survive and thrive. The easiest way I've found to provide food is to mix a slow release fertilizer into your potting soil before planting your container. I use a granular organic, all-purpose fertilizer into my soil. I also then feed my plants with a diluted, liquid fertilizer every week or every other week during the growing season.
Planting - There are two main things to know when actually planting a plant in a container (or anywhere else for that matter). You want the plant to sit at the same level that it sits in its nursery pot. So in other words, the level of the soil should stay the same and no more or less of the plant's stem or crown (where the plant and roots connect) should be covered. You also want to make sure there are no air pockets and your plant' roots are surrounded by soil. In a crowded pot, sometimes it is difficult to put soil in between the plants, but you will need to make sure that you do, or the roots will dry out if they are in an air pocket, and your plant can die. Sometimes you just need to feel around a crowded pot and stuff soil into any holes you feel. It's also a good idea to water a pot right after you plant it, which settles the soil. At that point you can go back and fill in any holes or depressions with extra soil.
Caring for your container garden - Watering is more art than science. You will need to know what conditions your plant or plants prefer. However, the majority of plants like to be kept in moist soil--not wet--but damp. To figure out if your plants need water, you can stick your finger down into the soil, up to the second knuckle. If your finger tip feels dry, add water. Be sure to water slowly and make sure the water is going to your plant's roots--not bouncing off the soil and running down a space that can form when the soil contracts, between the soil and the inside of your pot. You want to water deeply so the water gets all the way down to the plants roots. The best way to know if you've accomplished this is to water until it starts to run out the bottom of your container.