How can I draw my database design?

I think you can use MySQL Workbench, it's supposed to have reverse engineering (from database to model).

http://dev.mysql.com/workbench/

Have a look at MySQL Workbench, it's free and next release (currently alpha) will be major step forward (it will replace MySQL Query Browser).

You can do reverse engineering with Visual Architect or Power Designer but you have to pay.