There's a write up here on the steps to replace the clutch at
viewtopic.php?t=17517" onclick="window.open(this.href);return false; It involves removing the entire transaxle. You can not replace the clutch without removing the whole thing, bell housing and all.
As for rebuild vs replace, I don't remember hearing anyone rebuilding one. The consensus is that a rebuild is too labor intensive, and the parts cost too much individually to make a rebuild financially practical. Instead, folks tend to replace, and using a 5 speed from an 05 or later Vibe/corolla/matrix. Apparently the bearings in the 03's, and maybe the 04s were problematic and failed more than they should. Certainly did in mine
car-part.com lets you search junkyard inventories. Says there's one in College Park GA, out of an 08 for $1545. More than I paid for mine, but it is close by and from an 08, so theoretically low miles. Not really all that more expensive than any withing 500 miles of zip 30236. Another one out of an 06 over in Lawrenceville, doesn't list price but worth a call Without question more than you want to spend, but often junkyards will do the installs for a reasonable price.
If you do get a replacement from a junkyard, be sure to get some kind of warranty, to make sure the "new" one isn't dead on arrival