Molecular Biology of the Cell
It's not on synthetic biology, mind you, but presumably some understanding of the natural biology is a prerequisite to doing the synthetic stuff. Anyway, he works for GSK doing some pretty interesting stuff and is an all around smart guy, so I tend to assume his recommendation is a good one. YMMV.
I too think this is something to be on the curve of. You're gonna have to at least learn the basics of [organic] chemistry, genetics, molecular genetics and cellular biology. A blackbox approach will give you a very low ceiling.
Some books to start with:
Genes, Proteins and Computers
A Practical Introduction to the Simulation of Molecular Systems
It provides an unpretentious, solid introduction to core molecular biology theory, written in a personal manner by one of the 20th century's greatest biologists. And it's only $5 w/ shipping on amazon.
Read it, then go watch some of the short videos  by iGEM teams on their projects to get a sense of what's made possible by the synthetic biology approach.
The above doc aims to cover the basics of molecular biology projects in non-institutional environments. I suggest finding your local DIY group and hanging out with them for a while:
(Usually that just means "your local hackerspace".)