While You Stretch
Don't let your body take over. Your muscles will naturally take the "path of least resistance" to deflect away from a stretch. Even though you might be in good position, a muscle deflection means that you don't get a good stretch on the specific muscles you're trying to work.
For example, when you do a simple bent-over hamstring stretch and try to touch the ground with your hands, your knees naturally bend forward, compensating for the stretch you're asking your hamstrings to do.
Some knee bend is ok, but at a point you stop working your hamstrings by allowing your knees to take over and bend out too far.
Your hips are also a major deflection culprit because they have so many ways to rotate. Example: When you pull your leg back to stretch your quadriceps; don't let your hips push out -- which dissipates the muscle stretch and does very little for your legs.
Instead, focus on isolating the muscles you're working by maintaining proper alignment and balance.
Breathe! You'll find that by taking slow, deep breaths, your stretch will be much better. As you breathe, your muscles will elongate due to the increased oxygen running to them. It's natural to try to hold your breath while you stretch, and it sometimes takes conscious thought to overcome.
More: How to Improve Your Breathing on the Bike
Stretch Regularly
You'll find that the cumulative affects of stretching add up, just as if you were visiting the weight room or doing hill repeats on a regular basis.
And like the weights, it's important to stretch the same muscles more than once. Plan to do three complete sets, with the first an easy warm-up; then gently increase the stretches, holding them deeper and longer on the next two. You'll find that you have more flexibility after the first round.
Consider taking a yoga class for advanced stretching techniques. A class allows you to focus your full attention on stretching (typically for an hour), instead of the typical "stretch fast, gotta ride" mentality every cyclist is guilty of at one time or another.
More: Part 2: 7 Simple Stretches for Cyclists
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