How do elves die?

As elves are immortal, they can't die from old age. Hence the presence of elves such as Galadriel who have been around since the First Age during the War of the Ring. However, they can die from mortal wounds by sharp pointy things (i.e. if you stab one in the heart, he/she will die). When they finally get sick of Middle Earth they head off to the Grey Havens to cross the sea into Valinor, which I suppose could be seen as their "death"...

Does that answer the question?:P My Lord of the Rings knowledge has been a little rusty lately, need to reread some stuff.:D

If them be killed by somebody....

Elves are immortal, so they cannot die of old age. As explain above, elves residing in middle earth "go over the sea" to Eldamar, the place where elves dwell in Aman, where the Valar live, when the tire of Middle Earth. However, though they cannot die of old age or "natural causes" as we call it, and heal easily from wounds and hurts, elves may be slain or die of poisoning. Elves may also choose to give up their life.

Like what the others said, it's either one of them dies or if they gave up their immortality or depression...

They really never die or at least their spirits do not and they can be rembodied in the halls of Mandos and released again, they can die physically or slain from a wound and also of a broken heart or wounding of the fea(spirit) but they are bound to the earth and if it is destroyed so will they be.