You need two things: 1) a good feeling for the local prices and 2) experience.
Haggling is more than just quoting low prices. It about your complete presentation and attitude.
When they quote me their first price (I will never be the one to call the first price), I usually just smile at them, maybe tell them it is a ridiculous amount etc. So, while not quoting an amount, I am actually haggling, just not with words yet.
It's very hard to estimate the actual bottom price, however, (generally) they will not sell below their minimum profit margin. If you hit the real bottom price, you will know. After this happened to you once or twice, you will start to get a feeling for it. (and learn that many times before, they just made you feel like it was the bottom price, but it was actually not.)
If the starting quote is such a ridiculous amount that, if you bring the price down to half, you still pay too much: walk away. Not for show, but for real. As you say, you are worried about offending them, keep in mind they can offend you as well.
This may result in an instant drop in the price. However, if I walk away in a situation like this, they will need to be quite convincing to bring me back to the negotiations.
edited to add:
Don't forget, haggling can be fun! It's a very social activity; if you take your time for negotiations, it can be quite rewarding.