"... Shadowmourne must be hewn from piles of impure Saronite; the hardened blood of the Old God, Yogg-Saron treated only by master metal-shapers."
There are several clues here, one which is the obvious that whatever "impure saronite" is, it must be taken to Ulduar and somehow interact with the last boss, Yogg-Saron. Much the same way that Val'anyr had to be thrown into Yogg's mouth before slaying him. Perhaps saronite is imbued with Yogg's blood or yogg's blood is just another component. The words "master metal-shapers" might just be a NPC smith in Dalaran, but could also mean that you will need a fellow guild member to forge the components together, either a grand master miner or blacksmith.
With the weapon itself forged, we have this:
"... it is vital that Shadowmourne be drenched in the souls of the most potent servants of the Scourge"
To me this seems very self-explanatory; just go ahead, armed with the weapon, behead enemies in the Icecrown Citadel raid instance. The fact that it mentions "most potent servants" suggests that you have to slay an X amount of raid bosses. How many or what the exact process is, I cannot say.
"... Shadowmourne is to be adorned with fragments of the Frozen Throne."
Again, as the last step, very self-revealing prerequisite, in which you must face Arthas at the last chamber of the instance, and defeat him - multiple times, since "fragments" is in plural. And then, finally in the end, from all the trouble, you will eventually be able to receive Shadowmourne as a just reward. As a level 284 item, it will most likely last you a very long time. Way into the next expansion.
Sounds definitely worth the trouble to me.