To the person who arrived at this blog after doing a Google search for "cycling for the terrified" I hope you found something of comfort here.
Believe me when I say that if a nervous, anxiety-stricken person like me can cycle through London peak hour traffic ANYONE can do it! For many years I would not even get in a car, let alone ride a bike! Now, I do it with relative ease -- although I'm not sure it's ever wise to truly conquer the fear, because that's when you begin taking silly risks.
If you want to gain some handy tips, I can recommend John Franklin's Cyclecraft: Skilled Cycling Techniques for Adults. I bought this book about six months after I first started cycling and wished I'd bought it before I began: it's got brilliant tips for making difficult turns and how to improve your visibility in every day traffic conditions, among others.
But the best thing you can do is just go out there and try it for yourself. Practise makes perfect and all that. Good luck!