A 1/2IM was my first distance, too. I trained for about a month ahead of time, up at the Lake Miramar reservoir in San Diego, on an old Fuji 6 speed, and did the race on an old Klein Quantum 7 speed with no aerobars and which had the old SIS downtube shifters. Nowadays, I ride a 53cm, but that Klein that I borrowed was a 58cm, so you can imagine how badly I fit on it :-))
Not knowing a damn thing on how to train for tris, I used to do an hour hard bike, then eat an apple and run the 5 miles around the reservoir to top it off. I had never heard the term “brick” (which I was doing without knowing I was doing it) applied to triathlon. I always thought that that was what a basketball that clanged off the rim was called
I’d do that Monday through Friday, at lunch, then go over to the Navy air station at Miramar and swim in their 50 meter pool after work. On Saturdays, I rode 3 hours and on Sunday, I’d run 10 miles around the reservoir. For that month, I didn’t take a “recovery day” (I had no clue what the hell a recovery day was, anyway, so why do one?), and just took a day off the day before the 1/2IM, which I paid 25 bucks to enter. Naturally, I was so tired and worn out, and undertrained, I’m surprised I finished it, but my motto is “No Brain, No Pain” 
I guess I’ve proved you can do it, but man, I sure didn’t feel very hot, and staggered to a 5:27 finish. I fell down 4 times on the run (combined beach run on hard sand, then very soft sand then asphalt and a 4 loop 3.26 mile course). It was the Superfrog Tri, which was put on by the Navy Seals over at the Navy air station North Island.
Good luck, and keep asking those questions. Some of the best and smartest triathletes on the planet come through here and post advice. Of course, I’m one of the dumbest, so don’t pay too much heed to what I start telling you :-))
Tony