beginnertriathlete.com is a good place to start. There's a lot of information and resources, and I think there are free training plans as well. You might also want to check around in your community for a training group. Often YMCAs will run a training program. If you know which tri you are thinking of doing, you could check with the race organizers to see if they have any links to training groups.
And if it is primarily the run you are concerned about, you could start C25K now, and then follow that up with your tri specific training.
Good Luck!

Agree that beginner triathlete is a good place to start. The mentor programs are perhaps the best resource on that site.

My big issue that could course me not to reach my goal is the running. I can do short distance sprints but have never been able to run farther that about 500 metres before my back starts hurting. I've been told it's just weak muscles in my back.

I was where you were 2 months ago, and I have found good results through zone 2 training.
Run slow, and I mean r e a l l y s l o w. Slower than that, even. Your goal is to build running base, and a great way to do that is through zone 2 heart rate training, which is a PER of 3 or 4, tops, keeping your heart rate around 130 to 150bpm. I'm generalizing on the numbers, a lot, but there is a ton of theory on heart rate training, and zone 2 usually falls in that range for most people.

In two months, my pace has gone from a 12:45 mile to a 9:51 mile. Your body will adapt to the run, slowly but surely. Take very small steps, and try to keep the running form. At a 12:45 mile, for example, you can walk with a very long stride, but the point is to learn to run.

As for your back, you may want to talk to a doctor, and make sure you do your core work; however, you should be able to run for at least the amount you currently ride or swim, since those will use the same back muscles in a similar way.

Go slow, and it will come.

Even Dave Scott had to do a lot of walking when he started running by heart rate.