Interval training with minimal jargon:-
Alternating periods of hard work and gentle spinning. Helps build up tolerance to (some jargon) lactic acid and also raise lactic threshold.
In other words, you can tolerate pushing harder and the threshold at which it stops being sustainable is pushed higher. These two combine to allowing you to push harder for longer, giving you more time to sleep.
Effort should be constant throughout the interval, and the same for subsequent intervals in the set. This is nigh on impossible to do on the open road with just a Heart Rate Monitor as HR lags behind the body by about a minute. A power meter makes it a lot easier (since there's little/no lag) but it's still hard to maintain constant power on the open road unless you live way out in the sticks. Power meters are expensive (think £1000+).
A turbo trainer with a power meter is ideal (can be found for ~£400), or a gym bike with a reasonable accurate power output, with a bit of experimentation you can find out what power levels to do the various intervals at without visiting the vomitorium.
The ideal is that you want to finish the final interval wishing you'd never thought about doing them but having put in a constant effort over all of the intervals in the set. Failing to complete the intervals means you've tried to do too much, you're tired or overtrained, or you're coming down with a cold.
Using your levels:-
5 x 5 Intervals (5 intervals of 5 minutes each):
5 to 10 minute warm up at Easy
5 minutes at Hard (I1)
3 minutes at Easy
5 minutes at Hard (I2)
3 minutes at Easy
5 minutes at Hard (I3)
3 minutes at Easy
5 minutes at Hard (I4)
3 minutes at Easy
5 minutes at Hard (I5)
5 to 10 minute cool down at Easy
2 x 20 (2 intervals of 20 minutes each):
5 to 10 minutes at Easy (warm up)
20 minutes at Moderately Hard (I1)
Any length recovery period at Easy (usually 10 minutes)
20 minutes at Moderately Hard (I2)
5 to 10 minutes at Easy (cool down)
14 x 2 (14 intervals of 2 minutes each):
5 to 10 minutes at Easy (warm up)
2 minutes at Hard to Bugger This! (I1)
2 minutes at Easy
2 minutes at Hard to Bugger This! (I2)
2 minutes at Easy
...
2 minutes at Hard to Bugger This! (I14)
5 to 10 minutes at Easy (cool down)
There are many variations on these.
Warm ups should be at least 5 minutes long, cool downs at least 5 minutes, there's no real upper limit.
Pain is weakness leaving the body.
With a normal turbo trainer (with no power meter) pick a gear and keep a constant cadence. Check HR after 90 seconds or so. If it's too low change gears to make it harder. Too high (i.e. you can't maintain that cadence in that gear) then change down one. You're basically looking for the gears that you can keep pushing for 2, 5 and 20 minutes respectively before wishing that you could stop. Make a note of them and use them for the corresponding intervals above (two or three sessions a week depending on fitness). Obviously the shorter the interval the hard you can push for the duration of the interval.
You should find that, over time, you can repeat the same sets of intervals and your HRmax will begin to drop. When it drops enough you up the effort (up the target power by 10W or change up a gear) for the next set. Moving up too early will result in you not being able to complete the intervals at the new target power/effort. If you stick with it it'll keep going up although you'll soon run in to the law of diminishing returns.
They call this whole process: 'training'. Horrible idea.
Interval training is only part of it. I'd use it for the two or three higher intensity rides, but still doing a long weekend ride, and the 200k+ Audax each month.
P.S. It's the Bryan Chapman.