Depends on the faction.  With a lot of factions, there will be a
faction-neutral NPC you can do a repeating quest with in order to get your
faction up.  Or doing a quest for a faction you're already friendly with
will also increase faction with another faction that hates you.

It's all very dependent.  eq.Allazhazam.com is a good place to go to search
for faction-specific quests.  You'll almost always find a way to raise
faction with people that hate you, even if that means killing a thousand
mobs or doing a thousand turn-ins.

-Richard

Sometimes.  Not always.

Bard song and Enchanter spell for faction are self-only.  Grouping with them
won't help.  Many enchanters can illusion you, though, so if the KOS is caused
by race, that can help.  

It's pretty rare to be KOS based purely on race, though.  Illusions won't hide
religion or past faction hits.

If the NPC is charmable AND you can do the turnin when indifferent, this
usually works, and you get the faction for the turnin.  If you have to be
amiable to do the turnin, then you have be the one who charms the NPC to do
the turnin.

Most quest NPCs nowadays are not charmable, so this won't help.  It works in a
lot of old-world quests, though.  Other things that used to work but mostly
don't anymore are doing the turnin while invisible, or just letting the NPC
attack you and doing the turnin anyway.  Sometimes you had to start the handin
invisible, then click off invis and click "give" instantly after, and hope the
handin occurred before the NPC killed you.

And, as someone else said, a lot of factions have a way to build them without
using the KOS npc.
--
Mark Rafn    dagon@dagon.net    <http://www.dagon.net/>  

On Mon, 13 Mar 2006 18:38:20 GMT in
<w_iRf.648$tN3.164@newssvr27.news.prodigy.net>, "JK"
<greenmini@netzero.com> graced the world with this thought:

Check on Allakhazam, as Richard suggests, look up that particular
faction, they'll list how to affect it either way, if it exists. Seems
like some of them can even be something like sitting around for a
night killing some low or mid level trash mobs, probably faster than
most quests unless you find one that really give you a major faction
hit.