This topic was excerpted from Aging and Cycling, by Alan Bragman, D.C.
I have added my own interpretation of these thoughts further below.

"Initially you will need to take a very strenuous test to determine
your maximum heart rate (MHR) and set up your training program.
Before doing so, make sure to get the permission of your primary
health care provider. A max heart rate test should not be attempted
by a beginning or out-of-shape cyclist or anyone with medical
problems, particularly heart problems. One simple way to estimate
maximum heart rate is to subtract your age from 220*. This method
is not very accurate, however. It can produce a figure 10 or more
beats too high or too low.

A test to determine MHR can be done on the road or indoors on a
trainer. Either test should be done twice to confirm the findings.
To take the outdoor test, find a gradual hill about 2 miles long with
light traffic and no stops. Warm up for at least 15 minutes before
beginning the test. As you climb the hill, increase your effort so
that near the crest you're riding hard. During the last couple of hundred
yards get out of the saddle and sprint as fast as you can. The
highest number displayed by your heart monitor should be very close to
your MHR. If you live in a flat area, do this test on a windy day riding into
the wind.

For the indoor test, warm up for 15 minutes on a trainer. Increase
your gear every 2-3 minutes while striving to keep a 90-rpm cadence.
Push until you can't go any harder, and then sprint all out for as
long as you can. The highest number displayed by your heart monitor
should be very close to your MHR.

Once you have your max heart rate you can establish your various training
zones, which are based on a percentage of MHR."

For example, let's say you're a 56-year-old rider (me!)
with a MHR of 183 beats per minute.

Zone 1: 60-65% of MHR = 110-119 bpm for easy riding and recovery
Zone 2: 65-70% of MHR = 119-128 bpm for endurance and base mileage
Zone 3: 70-80% of MHR = 128-146 bpm for aerobic capacity training
Zone 4: 80-85% of MHR = 146-155 bpm for lactate threshold training
Zone 5: 85% + of MHR = 155+ for maximum aerobic training

My note:
*There's also the opinion that women should use the baseline formula of
226 minus age, so this may alter the zones slightly for this population.  I used
the formula 220 minus age for demonstration purposes.