I totally agree that driving here can be scary, especially when you are just starting out. People don't abide by the traffic rules, roads are often jammed, even pedestrians add to the difficulties.
Some things I would like to mention:
Stick to the rules: If others don't want to, it is their problem. Our life is in our hands and I have personally felt that it is best to obey traffic signals, wear the seat belt everytime, not put up tinted glass windows, not talk on the phone while driving, and follow the other basic rules that are absolutely mandatory.
One, it saves you any possibility of trouble with the cops. Two, if you ever get into a scuffle with another driver, you will naturally have an edge for the simple reason that you were the one who was sticking to the rules.
Lay off road rage: Ignore it in any form. Somebody's shouting at you for overtaking him, somebody can't stop honking because you are not giving him the space to move ahead (when there is none), somebody's looking at you angrily for a similar pointless reason, or whatsoever... IGNORE IT ALL. Indians are a very diverse people. There are greater cultural and wealth divides than you can imagine. So no two Indians are the same. Some can be really bad, some can be really good. Your aim is to ensure your safety. So if some idiot shows signs of wanting to pick up a fight or to mess with you, don't let him affect you and quickly take your own way.
Drive carefully: Be extremely attentive when driving. Drunken driving is a big no. Watch the road ahead, as well that on your either sides, and er, the one behind. Basically, be as careful as you can be. Before you start the car, tell yourself strongly that no matter what, you don't want to get anyone killed by you. That'll help you concentrate when you drive. It's not about getting stressed. It's about 100% attention to the task at hand because it can be dangerous.
So if a stray animal comes in front of you suddenly, or some poor kids, or some idiotic pedestrians, you will be able to apply the brakes immediately. 100% concentration = minimum response time
Don't speed beyond your comfort zone: Make sure that you don't speed up so much that you lose control. And losing control doesn't mean not being able to drive, it means being able to handle any situation whatsoever—however adverse and unforeseen it may be.
Practice: Whatever may be your doubts about Indian roads, so many people are still driving everyday and coming home safe. It's all about practice. Make a slow beginning, you'll gradually get used to it. I got used to it. It is more tiring than it should be, but it certainly isn't impossible.
Enjoy driving: Enjoy driving on the free stretches on the rare occasions when you happen to find them. And as soon as they are crowded again, get back to paining your legs with the constant braking-clutching-racing cycle. Don't forget, ultimately, you're gaining mastery over the skill. Embrace it.