Don't hesitate to just walk away. Any time you are feeling pressured or overwhelmed, there's nothing wrong with simply leaving the scene. This is standard practice in South Asia, so don't feel bad.
Keep your wallet in a tight pocket or other place where you can feel it on you. Often, the stress of bargaining is added to by a pervading paranoia about getting pick-pocketed. Lift that paranoia so that you can concentrate on the bargain itself.
Always attempt the fake walk-away. Again, this is standard is South Asia. Here's how it works: you ask for the price that you want, then the seller asks for a higher price. You repeat the price you want, and the seller drops his price a bit, but keeps it higher than the one you're asking. So you turn and begin walking away. More than likely, the seller will quickly call you back and offer you your price, or at least something much closer to it.
Find out how much a local would pay for the item you want. If you have local friends, ask them what they'd pay, or watch a transaction between locals before you attempt one yourself. Either way, knowing what the locals pay will help you avoid getting fleeced because you'll be able to begin the bargaining by naming a proper price.
Ask for a special price for several items at once. Often, a seller will drop the price significantly if you buy more than one item, then ask for one price for both. For example, when in a T-shirt store attempting to purchase four shirts, don't bargain over the price of one--bargain over a single price that includes all four. You'll likely see significant savings if you do.
Don't be afraid to be pushy! This is a tough one for many Westerners, but the truth is that this is, again, standard bargaining behavior in South Asia. A South Asian peddler or shopkeeper can spot timidity a mile away and will usually try to take good advantage of it--so don't hesitate to state your price firmly and say no to a counteroffer just as firmly.
Expect arguments--and don't give them too much credence. Attempting to pull at your heartstrings in order to get into your wallet is, once again, standard procedure in South Asia. It is to be expected.
Bargain around before purchasing an item. It's amazing how often a tourist will purchase something--only to find that the very next shop would have sold the same item for a third of the price!
