Growing plants - indoors or outdoors - varies greatly from climate to climate. Begin by researching and selecting plants that will thrive in your particular climate.
Choose Your Plants
Start by selecting plants that are hardy and will be able to handle a bit of stress as you learn to take care of your garden. Tomatoes are a great example of a fantastic beginner plant. All Tomatoes really require to do well is a nice spot in the sun. With a bit of online-research you will quickly learn when its best to plant your garden wherever you live.
Water when the soil has had a chance to absorb the water from your last watering. Depending on where you live this could be every day (like here in Arizona) or perhaps you only need to water every 2-3 days. The best way to see if your garden needs water is to just stick your finger into the soil - Get Dirty! - and see if the soil is still moist. Moist soil will stick to your fingers while thirsty, dry soil will fall right off your skin.
You can get away with just two pieces of gear. (1) A good hand trowel and (2) some good quality shears. Those two key tools should get you well onto your way to becoming a master gardener.
Soil and Containers
With a bit of quality garden soil from most garden centers at your local home-improvement store or local nursery you can start your garden anywhere you can find space. Wether you build your own raised garden beds or just use a few good solid pots and containers you can enjoy growing and harvesting what you grow.
So In Conclusion
...dive in and just give it a shot! It's really not that hard, and getting your hards dirty by playing in the soil of your garden can be so therapeutic, rewarding and calming. You'll love the pride and joy that comes with growing something on your own.