An interval is an amount of time where you work harder than the rest of the workout. If you don't have a heart rate monitor, it's more difficult, but you would need to be at least able to measure and describe your perceived effort.
Say, that your effort is on a scale of 1-10.
1 = super easy
2 = very easy
3 = easy
4 = slightly easy
5 = moderate
6 = slightly difficult
7 = difficult
8 = very difficult
9 = super difficult
10 - seems impossible 
So, you start out warming up for say 15-20 minutes at something between 1-5. Then for 4 minutes, you increase the effort to a 7-10. Then rest for 4 minutes back down to a 3-5 perceived effort. Then go again for 4 minutes at a higher perceived effort.
The increased effort can be from resistance -- more resistance on a spinning bike or a harder gear on a road bike. Or the increase effort can be from cadence -- you can increase your rpm (rotations per minute) from say a normal cadence of 80-90 to a cadence of 100+. With increased cadence, you won't have the heavy resistance and you are working a different "system" in your body.
I also like to do Muscle Tension intervals, which last about 10 minutes each, where I put on as much resistance/gear as I can stand and try to pedal in circles at a cadence of 45-55 rpm. It's a slower cadence, but resistance is very heavy like you are climbing a mountain. Don't mash the pedals. This type of interval has helped me to build strength similar to doing squats, but I get to do it on the bike. You can do 2-3 of these intervals with 5-10 minute recovery between each one. Perceived effort is in the 6-8 range.
In almost all cases, don't start out doing intervals so hard that you go breathless. You want to sweat, work hard, really feel the difficulty without running your heart rate into a red zone.
If you really want to seriously train, I think you should get a heart rate monitor and maybe a personal trainer for at least a few sessions to help you to figure out what your heart rate zones are so that your workouts are meaningful to your body systems. We're all vastly different in what sort of effort we would need to extend in order to be doing a true "interval" training.
----------------------------------------------------
"I never made "Who's Who"- but sure as hell I made "What's That??..."