I know exactly what you mean, as I too came to programming from a different background (I used to be a Mathematics Teacher).
The best advice I can give you is to build up your confidence by actually trying out programming exercises. When you're new to programming, the more "hands on" experience you can get, the more it will help your understanding.
I found the tutorials on the sun website very helpful. http://java.sun.com/docs/books/tutorial
also, the following book: "Teach Yourself Java" by Joseph O'Neil (Osborne books) is great for beginners, as it cosolidates your knowledge regularly with lots of short examples and questions.
Don't rush - you may have to cover things a couple of times. Once you have mastered a book like that, work your way through something more thorough and detailed, geared towards the Sun Java Certified Programmer Exam - there are some good recommendations on this website.
As to how long it will take you before you're ready to get a job in Java - it's such a personal thing, and also depends on the job. Sometimes the learning doesn't really begin until you start doing your first real job. I started off by working my way through the book above, and then applying to various companies as a junior Java Programmer, letting them know that I had taught myself, and that I was keen and able to learn. Don't get disheartened too soon.
Hope that helps,