Well, Kelemvorite clergy see themselves as having a very specific purpose, according to their god: they destroy undead, they destroy makers of undead, they handle the affairs of the dead (burials, last rites, execution of wills). That right there is the core of the religion from the less-populous side of the altar.
Worshipers usually come to Kelemvor after the death of a loved one, and a good number of them drift off to another patron after they're finished grieving. (nothing like Forgotten Realms to make dieties worry about worshiper turnover.

) Not so much silly ritual or dogma on their end, because so many of the worshipers wouldn't be around long enough to learn it.
Good aligned members of the faith take Kelemvor's stance on not allowing others to die before their time to heart, and will actively try to save people from violent ends, and heal those who've gotten close to said violent ends.
Neutral members of the faith tend more toward the affair-handling and information-spreading. Mark plagued ground, leave fair warnings about the trolls up the road, but if someone's stupid enough to ignore said warning well, it must've been their time. Best get to buryin' them. (would also note that this is the route that Kelemvor takes himself - he and his avatars will perform the sending at places where his clergy have no chance of going, and give the occasional fair warning.)
Evil aligned members of the faith tend more toward the crusading destruction of creatures that cause too much untimely death. Theory is, if assassin A would kill 10 people before his death, and Kelemvorite ftr/clr makes goo of him now, that's 1 untimely death, not 10. Such practice is fringe at best (hence that 'evil' part) when talking about redeemable killers (pretty much looking at the sentient races not marked as "always evil" in the MM there), but it's pretty well acceptable for all alignments if it's an irredemable killer (evil outsiders, undead, unintelligent creatures, etc.) - would warn, of course, that Kelemvor is LN, but he leans toward the good, and the LE member of his faith risks offending him if he gets a little too evil.
Lot of stylistic elements ended up swiped from Myrkul, in that Kelemvor swiped a lot of his temples and clergy. Old stuff is likely to have a skull motif, new stuff is likely to be gothic. Lots of greys and blacks, too: respect for the dead and mourning and whatnot.
...aaaand I think I'm out of steam.
//edited for spelling. *kicks English language*