Welcome to the club Fatma_sh! Cycling is a good way to get a bit of exercise everyday and you will get to see and know the city in a way which you never would while stuck in an underground tunnel. Plus, it is much more fun.
Don't be put off by horror stories, cycling is much safer than many people think it is, but there are things which you can do to protect yourself.
Other people have made good points already, although you are unlikely to learn the best ways to cope with traffic situations from reading a forum, the best way is to either do a cycle training course or just get out there and give it a go.
In my opinion the most important thing for your safety is your attitude. I try to put safety first in my mind, even if it means I end up waiting a bit longer at junctions or don't always go to the front of the queue. Don't always copy other cyclists jumping to the front or filtering up the left hand side!
There are times when you will have hairy moments but make sure you learn from them and try to think about what you could do differently to avoid the same situation in future.
I also always try to remain calm (although may not always succeed). There will be stressful moments and times when you feel vulnerable but keeping calm is almost always the best way to cope.
I think being familiar with your route is important. If you are going to be going the same way to work everyday can you walk it one day first and keep an eye out for any tricky junctions? You can then think about how to alter your route to avoid those difficult bits. Maybe you could do a trial run on your bike at the weekend when it is quieter before braving the rush hour?
I always carry with me: lights - I keep at least two front and at least two rear lights so if one fails I am not without. High vis vest - you don't need to splash out on expensive jackets, you can get vests or tabards for under £10 from Halfords (or other places). Spare inner tube, tyre levers, hand pump (although I have been cycling 50 miles a week for over 3 years and never had a puncture!) and a set of allen keys.
Don't forget the importance of good bikje maintenance! It would be very handy if you at least knew how to adjust your own brakes and change the pads. Depending on which borough you live or work you might be eligible for a free bike maintenance course through bike works (bikeworks.org.uk)