I'll try my best but the big advantage of the HR monitor is that it allows you to train at a nice steady pace and to train at different intensities. For instance on long slow runs you aim to run at 60-70% of your working heart rate and for harder sessions e.g. speed work you might want to train at 85%. There is a formula that does the math for you but many HR monitors do the math automatically.
The two important figures that you will need to know is your maximum heart rate, which is genetic rather than an indication of fitness (don't worry if you have a high maximum HR). The other figure you need is your resting HR, which is an indicator of fitness.
Are you keeping up so far? You are probably wondering how you get the above figures well for maximum HR you can use a formula e.g I use 215 - (half your age) + 5 (for being a girlie) but the best method for estimating your maximum heart rate test is to do a test. You can pay someone to do this on a treadmill or you can do this your self by running 200-300 m up a hill 4 or 5 times (make sure you have a recovery jog/walk inbetween).
Resting heart rate you measure first thing in the morning. When you wakeup pop your HR monitor on lie down and relax and use the lowest reading. You might want to monotor this over a couple of days.
Once you have your maximum heart rate and your resting heart rate you can work out your working heart rate zones. Suppose you wanted to work at 70% (a nice steady run) your maximum heart rate is 192 and your resting heart rate is 64. The forumla is:
(maximum HR - resting HR)*0.7 + resting HR = 70% of your working HR
(192 - 64)*0.7 + 64 = 154
Therefore if you wanted to run at 70% then you would aim to keep your HR at less than 154 beats per minute. Its actually quite slow and that takes a bit of getting used to but eventually your boday adapts and you get quicker. It should in theory reduce the risk of injury one of the biggest mistakes that beginners make to to do too much too soon.
John Parker does a much better job of explaining it in his book Heart rate Monitor training for the Complete Idiot.