If you click on this website.....
http://www.sugarontheweb.com/saga.php?rubr=4&srubr=9&PHPSESSID=a5c710dc6b77d4c24cd3c49cd360c648
it should help you.
Also from the website I got this for you
STAGES OF PRODUCTION
1. Delivery. The sugar beet is delivered to the factory by growers located within a 30-km radius. Storage time is kept to a minimum in order to preserve the sugar content.
2. Washing. The sugar beet is moved to washers fitted with agitator blades to remove soil, weeds and stones.
3. Slicing. The washed sugar beet is then put through slicing machines that cut it into thin slices called "cossettes".
4. Extraction. The sugar juice is extracted from the cossettes by diffusion in a long cylinder in which hot water circulates in the opposite direction to the cossettes. In a process rather like brewing tea in a pot, the sugar from the cossettes gradually passes into the water.
5. Purification. The juice extracted contains all the sugar from the sugar beet, as well as impurities (mineral salts) which are removed by adding milk of lime and carbon dioxide and then filtering.
6. Evaporation. The filtered juice contains around 13% sugar and 87% water. It is heated to boiling point and then passed through a series of evaporator pans to convert it to syrup containing 65-70% sucrose.
7. Crystallisation. Tiny sugar crystals are added to the pans to start crystal formation. The mixture of crystals and syrup (or "mother liquor") is known as "massecuite".
8. Centrifugal treatment. The massecuite is spun in centrifuges to separate the sugar from the syrup. The sugar settles on the sides of the centrifuge and is then washed with clean hot water to produce white sugar crystals.
Extraction is just part of the production. Hope it helped.
In West Indian History, beet was one product used to produce sugar. I do not know if they still use it today.