Triathlon is not a big scary monster. The choice to make is Sprint vs. Olympic length for your first race. My suggestion is to do a sprint, as the swim is very short (this is the most daunting part, as the swims are almost always in open water) with a probably 20mi bike a 3 mile run.
Last summer I spend about 5 weeks with 2-4 swims a week and as many runs. A couple times a week I'd head up to a gym and get on a stationary bike.
There was actually a dude that was easily 300+ pounds, probably 40% bf or something, and was cruising right along.
All you need to do is get your body used to doing a specific aerobic exercise for as long, plus a little extra, as you expect part of the event to take you to complete.
Training has to be different for everyone because, as if you read any Tri info from other athletes who do it, everyone has different strengths with different parts of the race.
For me, because I have a background in cross-country, I was able to run a little less (b/c I know how to run) and focus a little more on swimming, which is a better aerobic workout and easier on your joints if, like me, you're overweight as well as out of shape.
So, I went from couch potato in the end of June to Triathlete in the second weekend of August. The biggest thing you need to do is spend time in each event at least twice a week, and by the time the race (and, really, do a Sprint your first time) arrives, be able to comfortably do each leg for the length of time you expect it to take you, plus a decent buffer (as you will undoubtedly race harder than you train).