One very basic and important aspect of interval training is that you DO NOT go at "close to max" or to "just short of booting" at least to begin with.
You might be at that point on the last rep, but not the first.

Regardless of the duration of the interval (could be short-ish, could be long-ish... with designed rest in between) is that you do a set of 3-5 reps generally. Just an example, let's say 4 reps of 4 minute effort/90 second minute rest, for a total of 15-16 minutes of "hard time". You'd warm up for 5-10 minutes before and do a 5-10 minute aerobic cool down afterwards. The amount of "hard time" might get progressively longer as you progress, maybe adding a rep and/or making each a little longer.

The basic concept is that you start with your first interval at an effort such that you can duplicate it for the full 3-5 rep workout. Let's say you're doing a hill. If you go balls to the wall on the first effort, say doing it in 3 minutes, you probably won't be able to do that 3 minute time 4 times in a row. You'll probably find yourself slowing down each time, and maybe really struggling on the last one.

You need to pace that first effort so that you can still do it in about the same time for another three repeats. They should be more and more difficult to duplicate every time because you're getting tired, and the very last one should be very, very difficult to achieve. That way you know you're really maximizing your set. It might seem too easy at first, but if it's really tough on the last one, you'll know that you've done it smart.

I haven't read the links above, but this is the way it was taught to me by very qualified running and skiing coaches. There's more to designing the intervals for serious, well monitored training and specific goals, but if you follow the principal of being able to repeat it for 3-5 times with a modest rest in between, and the last one is really, really tough to achieve, about as much as you can do, you're probably getting a huge portion of possible benefit from your intervals.

Oh, another thing is that this sort of hard workout (including race pace sessions and races) needs to be only about 20% of your weekly schedule. You need to be rested to get the maximum benefit out of the hard days. You also need to rest (easy days, days off) for your body to absorb the training. Many cyclists especially think they are being tough and effective just riding as fast and hard as they can every time they ride. It might be tough, but it's not smart.