Okay, everybody plays CoC for different reasons. For me, it's an adventure game with horror themes set in the interwar years with close-to-normal-people ranges of ability for the characters.
It's also a game a lot of folks really love, and a distinct number of other folks have tried to play, only for it to end in deep frustration.
Here are some things that I've done that may help that second group of people.
1) Make sure you and your players know what you're getting into ahead of time.
I started playing in the early/mid 1980s with folks who'd mostly played D&D or other TSR adventure games. Today, folks have other backgrounds in games. Try to explain this thing in reference to what they already know.
2) Decide how long you intend to play the characters.
There's a very different and worthwhile approach to making characters for a one-shot versus a short campaign vs an open-ended campaign.
For a one-shot, you may just plain want to use pre-gens. Fictional ties to the adventure aside, build them with high level, relevent skill sets, small in number, using the chargen rules as guidelines or ignoring them entirely.
It's an old game. For any non-combat skills, give them much higher score, since they'll tend to be rolled less frequently. That Punch or Pistol score can be half or less of their skill in Chemistry, since they might roll that combat score 3-5 times in quick order in an action scene, where that Chemistry skill might only be used a couple of time during the entire adventure.
Modify this approach the closer to book chargen rules the closer you get to wanting to play a more traditional open-ended campaign.
For faster play, consider lumping some skills together, especially research skills. Or even go a little pulpy: Have a character type figure out first, have the players allowed to buy a group of skills up to 40% as a whole bundle, then have them spend on individual skills beyond that.
Know where you want things capped. Buying skills to 40-60% should be easy. After that, it should become much harder/expensive, and vastly harder after 80%.
3) Treat non-combat skills as Saving Throws or Quality Check rolls, and decide for your purposes what constitutes a professional level.
IIRC, it used to say that 40% in a skill constitutes a professioal level. Treat that as a a minimum. For those familiar with Trail of Cthulhu, that would be like saying the character simply has the skill.
As Quality Checks. If you have the skill and there is a relevent clue, you get it. Any roll against the skill is basically a secondary quality check. Did you get extra info, did you do it quickly, did you do it without drawing attention to yourself, did you do it without wasting somekind of resource? If mulltiple characters have the skill, rolls can be used to determine which gets the clue, if your players like that sort of thing.
As a Saving Throw: Only when things are truly FUBAR should players be required to roll, and then DO NOT modify the skill. I don't care what the book says. Only on a truly remarkable failure should anything directly dangerous come of a failure even then. Everything else is tough complications.
4) Again, depending on how you play, giev players an idea of what you're going for.
Me? I'm a softie at the beginnning of an adventure and more hardcore towards the end. That's really how I think of normal CoC. Communicate your approach. Also point out that CoC really isn't a period-sandbox for the most part. When you agree to play a CoC game, by implication, your characters are involved in hunting down this mystery until they've resolved the threat, been destroyed one way or another, or basically admitted defeat and retreated completely away and given up. Those are pretty much the core options for PCs.
Alrighty, y'all gimme yers!