A proper warm-up will prepare your body for the workout or race, and will make the work feel easier than it would if you started out cold on your bike.
Basic warm-up: (first 8-10 minutes):
Now, you should do your stretching. It is generally accepted that it is better to stretch after your body has warmed up a bit, than when you are cold. You will feel more limber and your muscles will stretch better because they are warmer.
Pick a handful of stretches that you can do using your bike. Make sure to stretch out the lower and upper back, legs and any parts of your body that feel stiff or sore.
For the rest of the warm-up:
At this point, you will be fairly well warmed up, and what you do next will depend on whether you are warming up for a race or just a workout, and if the latter, what sort of workout you plan to do.
If you will be doing a workout that does not include high intensity cycling, then you can go ahead and start it now.
If you will be doing an interval workout that requires high intensity cycling, warm up for about another 5 minutes. Cycle steadily for a minute or two at moderate intensity, then do a few more bursts, working up to the intensity of your intervals. You should also increase the length of your bursts to 30 strokes or a minute long.
If you will be racing or doing a time-trial, 15 minutes may still not be enough warm-up. It is important to do some bursts of closer to 2 minutes in length at race pace that really make you feel tired.
It is also a good idea to do several shorter bursts at faster than race pace so that it feels easy when you settle back down to your target pace. Finish it off with a few minute of relaxed cycling, and you will be ready to go. Try to finish your warm-up as close to the start of the race as possible.