I believe that I have figured out the meaning of life (serious) and I would like to discus the matter with the Holy Father. What channels do I need to go through and steps need I take to be granted such an honor?
Maybe you should start with your priest and work your way up.
Or you could write to the Papal Nuncio, who is the senior diplomatic representative of the Holy See to the United States.
His Excellency Gabriele Montalvo
Embassy of The Holy See
3339 Massachusetts Ave., NW
Washington, DC 20008
Hmmm…You’re probably aren’t the first one to believe so. Could I suggest to discuss the matter with a somewhat more accessible individual first? Having an audience with your local bishop probably isn’t easy, but at least should be actually possible. Then, if whatever you figured out is truly earth-shattering (which I strongly doubt. How many billions people already have thought deeply about the meaning of life, how many thousands of the greatest thinkers wrote done their opinions about this issue, which are available to all at the nearest library?), I assume he could recommand you higher up.
Of course, the regular papal audiences, open to the general public, do not include any sort of private chit-chat with the pope. You just get to see him from a distance.
Well, what is it? don’t leave us hanging man!!
The Pope supposedly has the direct line to God. If you’ve really figured “it” out, and the Catholic religious dogma is correct, the Pope should call YOU, no? God can arrange the interview if He feels it necessary.
Alternatively, if you’ve figured it out and the Catholic religion isn’t correct, why tell the Pope at all? He has a vested interest in not believing you.
This sounds flippant, I’m sure, but I mean it to be factual. Given my limited knowledge of the Pope’s position in Catholic belief, shouldn’t this just all work out automatically?
I do hope it’s all your own work. 
1-800-POPE
If you’re right, you win a speedboat.
Seriously though, I’d agree with what other posters are saying. Presumably you’re Catholic? I would think that talking to your local priest would be the way to go and if he agrees that you really have something (and who knows, you might) he can advise you where to take it from there.
If he doesn’t, so what? You’ve found a meaning in life for yourself, and that’s all that should really matter IMHO.
Generally speaking, people of high visibility attract a lot of attention from random members of the public. I work at a government agency, and we get calls every day for officials whose name is in the news.
No offense, but frankly, many of those who actually expect to talk directly to the Number One Guy are mentally unbalanced or extremely obsessed. We get people all the time with cases like these: they think the government is trying to kill them, or they were irradiated by aliens, or they were hurt in the nuclear explosion the Soviets set off in Sicily to assist in Christ’s return, or stars outside Earth’s atmosphere are causing helicopters to crash.
Almost without exception, these lost souls want to talk only to the Number One Guy directly, and reveal the “punchline” of their message to him. Of course, the Number One Guy can’t spend all his time listening to this kind of thing on the off chance that there’s a diamond hidden in all that rough.
Mostly, people who are not somehow disturbed seem to understand that there’s a screening process so that the Number One Guy doesn’t have all his time taken up by idiots, obsessives, and unbalanced people. Such poeple are willing to go through the normal chain of command to get real help.
If you have something important, saving it just for the Pope will – to be brutally honest – probably result in your never receiving said audience. Millions of people probably want a private audience, and lots of them might be willing to say anything to get it. He’s probably much more patient than the public employees at the agency I’ve mentioned, but there are limits.
However, if you have a good enough idea, and you make it publicly known, the Pope might well come to YOU to talk about it. Smart people with problems that need solving – and certainly the Pope has a lot on his hands – are always looking for new ideas and willing volunteers to whom they can delegate.
But they need to judge whther it’s worth their time first. They need to see the idea for themselves. That means it has to get through the screeners, not by bypassing them or fooling them, but on its true merits.
Send your idea up the chain of command; if it’s good, the Number One Guy might come talk with you.
Sailboat
Campaign contributions, I guess.
Here is a link for a page to request a ticket for a papal audience. I think, though, that an audience is not one-on-one but instead a small group of people with the Pope. I think you can greet him briefly but don’t think you can talk to him for an extended period.