This is some *very* basic advice if you've never done a horror RPG. Much of it may be (too) obvious... but my experience has been that running a horror game can be very different from running an adventure game. 

1. Monsters are more scary the less you see of them (c.f. Jaws). In D&D, you see "An Owlbear" In CoC, you typically don't see the whole thing, have no idea what it's name is, and get descriptions in terms of decay and elemental revulsion.

2. Related to the above: in D&D, you run into the monsters right away, and keep running into them until you're through the dungeon. In CoC, running into the monster is probably the last thing that's going to happen in the game... so timing and pacing are critical.

3. As a result of 1 and 2: You need something not-boring to do in the game before you run into the monster. In many CoC games (and stories) this involves investigating a mystery. A common setup is that there are clues to what's going on on and what kind of threat is out there -- and if the PC's are smart and lucky enough, they can use the knowledge they've learned in the investigation to win (This time...) against the horror.

4. If you decide to go with an Introduction -> Investigate -> Reveal / Climax -> Everyone Gets Eaten kind of basic story line, you need to make sure the Investigation phase doesn't go too slowly or get boring. Some quick points

A) Don't have the game hinge on finding one clue -- or on *understanding* what a clue means. This sort of thing is very common in mystery *fiction* but in RPG's it often results in the game grinding to a frustrating halt since the PC's missed or misinterpreted the clue and have no idea what to do next

B) I find that PC/NPC interaction is more entertaining than forensics -- so my "investigations" tend more toward questioning suspects than searching murder scenes or the like

C) Try to build tension -- there are lots of ways to do this, but the game works best if the PC's feel that their actions are driving things toward a shattering climax. You can do this with mini-climaxes (e.g. First you fight the cultists... Then you fight the Shuggoth, and finally you fight Cthulhu, himself, or whatever).

Another good way to build tension is to put the PC's on a clock (e.g. if you don't solve the mystery by the Solstice, they're going to summons something *horrible*)

5. Be as scary as you can be without running off your players. To a certain extent, you're telling ghost stories and people are there to be scared (if this is the first time playing, that might not be the case, but in general, that's what folks like about CoC) -- there's lots of good advice (and whole threads) on being creepy.