been here, experienced that..
a few pointers from someone who's driven in both cities quite a lot -
lane discipline: there is no such thing in a'bad. You take whatever lane is available. Also in Kolkata when someone in front of you in the lane breaks, you break as well. In A'bad, you don't necessarily break, you move into whichever lane is available at that moment. This is the primary cause of accidents for new comers to the city. You might be driving in your own lane and suddenly someone will try to cut across into your lane because the guy in front of him slowed down
Signals: there are a few places where it is monitored and you are expected to stop, most other places is a free for all. The trick is to slow down just enough to check if - a) there are any cops manning the signal, b) do other drivers coming from the other directions stop. If neither of these things happen, you go don't stop either. If you decide to be extra nice and stop at all signals, just deal with the honking
getting past a crossroad: since no one stops at the signals, it's a free for all when it comes to who has right of way (answer here is 'no one'). If you drive a car and there is enough space in front of you for half of your car to occupy (even if that means the traffic coming from the right will get blocked), you take it. If you decide to be nice and let the others pass (because hey, what's the hurry, you go I'll wait), you will be - a) waiting there for ever because no one else will now give YOU the way, b) dealing with a lot of honking
tips: don't let it get to your head. People here are generally speaking nice. But the road / driving sense is pretty much what it would be for a city that has grown too big too quickly (pune, bangalore). Add to this the obliviousness of a few who will stop in the middle of the road to ask for directions or veer from left to right because they don't know if they are in the right place, and you have a lot of frustration on the road. There is no point in getting angry or distraught that others are honking at you. Roll up the windows, play the radio at a volume loud enough to drown out the honking noise and accept that there are a few of us alike who are just dealing with it