Here's how it works:

The system uses different units, much like our standard system does... where we have feet, yards, and miles, the metric system has centimeters, meters, and kilometers.


If someone were to ask you to switch 8583feet into miles, you'd probably need a calculator, but if they asked you to switch 8583meters into Kilmeters, you could answer easily: 8.583

If the metric system is so much better, why don't we use it?  The US has long been the world's leading economic power, so it has the luxury of laziness.  Actually, we really are on our way to becoming a metric nation.  Anyway, on with the info...

The metric prefxes I acquaint my freshmen with are as follows....

Kilo
Hecto
Deka
---base unit--- meter, gram, liter
deci
centi
milli

The system is so easy because between one step and the next is a factor difference of ten.  This means that if you have 10decimeters, you have 1meter.  If you have 4.7Hectometers, you have 47Dekameters.
Compare this with our system.... if you drive half a mile, how many feet is that?  how many yards?
Once you become familiar with this system, you appreciate its simplicity and wonder why you grew up using units that came from ancient Egypt.

Now, if you jump two steps in the scale above, that's a factor difference of 100.  So if you have 333decimeters, you have 33300millimeters.  Easy enough?
 
kilo 1kilo=1000meters 1meter=.001kilometers
hecto 1hecto=100meters 1meter=.01hectometer
deka 1deka=10meters 1meter=.1dekamater
BASE
deci 1deci=.1meter 1m=10decimeters
centi 1centi=.01meter 1m=100centimeters
milli 1milli=.001meter 1m=1000millimeters

You could go on and on with this table, but what's the point?
If you have 30hectometers and need to know kilometers, what would you do?

30hectometers * 1kilometer/10hectometers = 3kilometers

Solving problems in this way is called dimensional analysis, and is described here.
If you think you get it, try this.