I've had this on the farm where it was harvested, and was able to verify for myself that wild, happy civets were left to their own selection process and merely followed around by farmers eager to find the drops.
It's not unlike any other Arabica bean. What I had was single-source, but that's rarer - farms doing it correctly don't produce a lot, so packagers and marketers will usually buy from dozens. That brings me to the first thing that determines the taste of it:
Some farmers roast themselves, others just sell the beans. Many sell directly to people and to packagers, so unless you get it single-source, you're probably going to have a bag of beans roasted anywhere from blonde to nearly dark. If you're serious about tasting it, find a place that offers single-source, or roasts their own. You want it just at the second 'crack'. A comparable color is a Starbucks 'blonde' roast, or the usual color of illy in the red can.
I've had it two ways, as espresso and in a press. I prefer to have it in a press, despite not getting nearly as much crema. A coarse grind, hot clean water and about 4 minutes to brew. Drink it immediately with a clean palette. Make sure you're not thirsty, make sure you're not hungry, and make sure there's nothing going on with your taste buds other than the coffee. You want to sip slow and enjoy it. Don't let it get cold, but slow down.
While debates are quite hot regarding whether or not the civet's digestion of the bean adds anything to flavor, I'm quite confident that the selection process does. Good Arabica coffee is known for the subtle nutty / caramel hints, and you know it when you drink this. I couldn't detect any difference in acidity, but the flavors that the bean is known are definitely more present than usual. This makes a lot of sense given the selection process, civets are very picky cats.
But, that's not to say that a very discriminating and trained picker couldn't get you something close. In fact, illy (red) comes very close to the same quality and presence of flavor undertones that I've experienced with alamid (kopi luwak).
Don't raise your expectations too high, it's not really that much better than any other very high quality Arabica. You're paying for the process (make sure you're dealing with an 'honest' source) as much as you are the quality of bean, novelty and experience.
It tastes very good, but so do the illy beans I grind every day.