"What sorts of equipment do I need?" you might ask. Surprisingly, not a lot to begin with. Start with the basics. Then, if you really like it, you can go from there.
1. Running shoes
Go to a specialty running store. The shoes won't cost anymore than if you get them on-line, and they have running experts to watch how you run and fit the shoe to your foot. This has prevented so many injuries for me. Running in the wrong shoes is a recipe for disaster. Remember to get new shoes after 300-500 miles or so (usually about 4-6 months, unless you're a marathoner). They won't look worn but the cushioning will be shot. It makes a huge difference. I got really bad knee problems from running in old shoes (only 9 months old). New shoes, happy knees. Once you find the shoe that works for you, don't change it. Your feet will thank you. Also, running socks are important. Find a non-cotton, wicking fabric; this will prevent blisters. Makes a huge difference, believe it or not.
2. Bike and helmet
You don't need a fancy bike. If you have a mountain bike, hybrid, or old commuter bike, use it. If you get more serious, you can always trade up. I will be honest; a road bike is ideal. Speed is the key, but if you're just doing it to have fun and finish, who cares? Take it to a bike shop and get a good tune-up. Get it fitted too. This will help prevent injuries. I would recommend switching the tires from the knobby thick kinds to the thin, road-like tires to help you go faster. Otherwise, your legs will be exhausted by the end. Also, put the strappy-thingies on your pedals to make your pedal-stroke more efficient. Then, you can pull up and down. Your legs will feel like they're going in circles, not pumping up and down and just pushing.
3. Bathing suit, goggles, cap, and pool access.
The pool is often the most intimidating part for new triathletes. Many local YMCAs have master's swim classes. Master's doesn't mean "expert." It simply means, "adult." These are great for learning how to swim correctly and are also a lot of fun. Check out your local pools. I have listed a good link for finding a pool in your area. Freestyle, or crawl, is the preferred stroke in a triathlon. It's the fastest and most efficient. However, you will see a lot of people doing breaststroke and backstroke. The swimming phase is commonly the most difficult for triathletes. Remember, you don't have to be an expert swimmer b/c there are 2 other phases! In your first triathlon, you will see people resting on the wall or jogging through the water. All this is perfectly allowable. You just can't get help from another person, or be pulled by a boat. But stopping and resting is perfectly acceptable. Many people do it. And believe it or not, your freestyle WILL get better so keep trying in practice!
4. Race suit
For a sprint triathlon, you won't have time to change from your bathing suit to your bike clothes in the transition. Most people were a triathlon outfit that is made for all 3 phases. I wear a tri top and tri shorts. They can go in the pool, but the shorts have a small pad to help cushion my butt on the bike. If it's cold, I pull on a shirt in the transition area after the swim.
Sunglasses (also good for keeping bugs out of your eyes on the bike), sunblock, visor, lots of fluids in water bottles that you put on your bike (I like Propel instead of water; it makes my tummy happier)
That's all you need to get started!!!
More on racing and training later. Hope this is a good start.