It depends. For anyone with experience in web technologies, I would recommend 1 to 2 months.For a complete novice, I would say 3 to 6 months. But this is just my estimation.There are many factors to be taken into consideration like the grasping potential, amount of time that can be spent per day, the balance between work and personal life and so on. YMMV.
Regarding the books, you have 2 options
1) Head First Servlets and JSP - Follows a new,wonderful approach that makes learning, an enjoyable event.
2) Manning's SCWCD 1.4 study guide - Follows the standard study guide approach which many find comfortable.
You can choose one or both of them. Also don't forget to read and refer the specifications in combination with the above books.