Before Arwen's birth Elrond wielded Hadhafang at the end of the second age of Middle-Earth, during the Last Alliance of Elves and Men in the great battle against Sauron. Later his daughter Arwen used Hadhafang when she aided Frodo in his escape from the Ringwraiths.
Inscribed on the blade are runes in the Elven language of Sindarin that say "aen estar Hadhafang i chathol hen, thand arod dan i thang an i arwen." Which translates to "this blade is called Hadhafang, a noble defense against the enemy throng for a noble lady." The original inscription included the last line "Idril i hel en aran Gond dolen," which translates to "Idril, daughter of the king of the Hidden Rock (Gondolin)." It was dropped from the finished prop due to a lack of space.
There is an intentional pun in the inscription - the Sindarin translation of "noble lady" is "arwen", so in effect, the blade claims to be for Arwen, even though it was made for her grandmother.
Above from a UK reseller's site, quite nice:
(blurbage is likely official, but this is the longest edit I found)
And some larger images of the sword (1000x184) and it's pommel (680x313):
Also from the UK reseller's site above, double plug:
Again, this material is likely official, but these blokes put up the most of it I found.