Welcome to BT and the multisport community.
BT has a number of articles to get beginners on the road to their first race.
Gear: What's required is a functional bike, bike helmet, an outfit you can swim/bike/run in, running shoes, and maybe a pair of goggles. I did my first triathlon wearing a pair of swim trunks, pulled on a cotton t-shirt after the swim, rode my steel framed mountain bike wearing my running shoes, and then ran. It was a blast, and I've been hanging around ever since 2005.
I've since picked up a road bike, a tri-bike, clipless pedals, wetsuit, tri-shorts, tri-suit, heart monitor, lots more workout wear, etc. There's time to *eventually* get all that stuff.
Training: Start out easy. Start out carving out time to train. You can actually combine the two if you set aside 30 minutes a day simply to walk. Then, you can start running some days, biking some days, swimming some days. Every one of those workouts you switch from walking to something else...go easy enough that you will feel like doing the workout again (so you can do it again tomorrow).
Swimming: No idea what your swimming background is. Swimming is very technical. Unless you're starting as a "proficient" swimmer, consider getting some swimming lessons/coaching. Learning good habits is much easier than unlearning bad habits. I was a lifeguard and swim instructor a l-o-n-g time ago. Here's something I see regularly in new swimmers: Get in the water, apprehensive...swim as hard as you can hoping to get to the far end of the pool (often without putting your face in the water), hang on the end gasping and panting and thinking "I am shot after 25 yards...how am I going to swim 600 yards???"
Goals: You'll hear many people say "don't set a time goal..." If you've got goals (and you SHOULD) OWN THEM! Be willing to share what they are with others. However...put them in context. It's OK to have a goal of doing your sprint tri in 1 hour 30 minutes (if that's what it is). But also know that whether you hit your goal time or not, you aren't likely to lose your job or your house and your family and you dog will still adore you as much as before. Now...if you keep your time goal secret and then abuse your family and kick your dog because you didn't hit that "secret" time goal, they will have no idea why you're upset. (I really advise AGAINST this approach.)
So the final and somewhat related bit is ATTITUDE. Be gracious and be thankful that you have an opportunity to race no matter the results. Thank the volunteers. Thank the officials. Thank your family. Chances are, there will be other participants as anxious as you are and there will be participants calm as a cucumber.