First, I highly recommend giving this page over at Unequally Yoked a read. In summary, the author examines two conversion anecdotes, one from a Christian and one from a Mormon. She makes the point that, while both seem quite sincere, they are either mutually exclusive, or God doesn't give a rip about which church you join (or perhaps, more charitably, God directs different individuals to different churches). This seems in stark contradiction to the religious tradition of every major religion, essentially all of which claim to be the only way to God. The point that she calls out very nicely is that this causes us to ask some very difficult questions- firstly, is there any way of differentiating a true conversion experience from a false one, and secondly, if there's not, what does that say about God? In point of fact, it says that he places us here, expects us to get the right answer about who and what he is, but gives us absolutely no way of differentiating a conversion experience to the correct religion from a conversion experience to the incorrect religion. Unless someone can offer up a convincing filter for religious experience that passes the conversion stories of one and only one religion, this problem seems very, very difficult to overcome.
At this point we must ask ourselves, what would be considered "good enough" evidence for God? Certainly God could show himself in a clear and persistent way (i.e. he could come down in a physical manifestation). Provided that manifestation was clearly supernatural and remained in perpetuity, that would probably work. But then again, maybe not? Maybe we would study it and doubt it and be skeptical of it until we managed to find a reasonable explanation for how this pillar of fire that could talk existed. A more likely argument against this, I think, is that this does seem to relegate God to the role of lapdog, somehow tied to our beck and call whenever we want reassurance of his existence. If I was God, I'm not sure I'd be cool with that.
Miracles provide another possibility. Essentially every religion claims to have the power of miracles on their side - indeed, most early Christian theologians say that we ought to be convinced of the truth of the Bible on the strength of Miracles and Prophecy. But curiously, all substantive, verifiable miracles have happened in periods of history where there was little to no scientific skepticism, and a great deal of religious fervor. And there have been none (that I know of) since I've been alive that can be conclusively classified as miracles. As Ethan Allen wrote, "In those parts of the world where learning and science have prevailed, miracles have ceased; but in those parts of it as are barbarous and ignorant, miracles are still in vogue." While this does not disprove God's existence, it certainly casts a bit of a shadow, doesn't it? Why go from performing all kinds of miracles to performing none, and at a time when we seem to need them the most?
Bear with me here as I take a bit of a tangent. Let us consider the case of two new clinical tests. These tests will tell us if you have contracted a disease which is highly contagious and highly deadly. Each iteration of the tests is independent (no one is systematically untestable by either test). Test A has a 95% chance of catching the disease, and a 5% chance of giving a false positive. Test B has a 100% chance of catching the disease, but a 15% chance of a false positive. If you're administering this test to thousands of people, which do you choose? In this case it seems pretty obvious to me that a false negative is much more costly than a false positive, and therefore test B is far superior for our intended use.
Let us apply this logic to the question of God. Clearly we're dealing with a binary distribution here- either there is a God or there isn't a God. But which is better, a false positive or a false negative? Do we want the highest overall certainty that we're correct, or do we want the highest chance that we catch the positive case? The easy answer here is to bias towards a God, because the cost seems much higher if we're wrong. But on the other hand, religion has the option of making the cost of a false negative arbitrarily high (say, eternal suffering and torment). If what they're after is converts, isn't it in their best interest to make the cost as high as possible? Should we really be kowtowing to threats? (bonus points if you didn't have to look up the word kowtow)
I bring this up not because I have an answer, but because it's an important question. If we're biasing towards catching 100% of the cases where there is a God, then color me a Christian, because I am not 100% convinced that there's NOT a God- but that's mostly because it's impossible to ever be 100% convinced of that. This is the logic offered by Pascal's wager (If I'm wrong I lose nothing, but if you're wrong you lose everything). But this fails for me three counts. First, Christianity is not the only religion that claims eternal damnation for those who don't fall in line, and therefore this argument gets us no closer to picking a God amongst the many options. Second, taking a test that catches 100% of positives but also gives 100% false positives is the same as taking no test at all. The function of the test is to exonerate the disease-free just as much as it is to catch the diseased. Third, I simply resent the threat. I don't think fear should be the motivation for anything we do, much less choosing a God (who by the way, supposedly loves us). It strikes me as a method of control, not as a legitimate argument.
Finally, we must tackle the question of internal conviction. As previously discussed, every faith has believers with authentic sounding conversion stories. In this way, they at the very least negate each others effectiveness as an apologetic tool, and at the worst are a condemnation of the idea of a non-generalist God. However, we must consider the case where you yourself feel such a conviction. In light of the fact that humans are clearly capable of experiencing earnest but false conversion episodes, are you justified in believing one of these episodes if it happens to you? My answer here is a weak one. I think you need to be highly suspect of these episodes. I think you need to verify them against other experience. I think you need to see if the conviction lasts a few weeks, even months before making any real decision (my general theory on life includes not making big decisions while you're in a highly emotional state). But ultimately, I think you must judge for yourself the strength of your own conviction. I think a person is rationally justified in believing something if they are strongly enough convicted about it. Particularly in the case of Christianity, which claims just this experience as justification of it's truth.
My ultimate conclusion to the question "how do you know?" is that you don't. In fact, you can't, because with the supernatural you have no objective standard by which to measure truth. I suppose this is the point and purpose of faith.
Each of us must therefore account to themselves what level of conviction they deem compelling enough to accept as truth. For me, it concerns both intensity and duration. I must be convinced of the truth of my conviction with such intensity as to have no choice but to believe it, and this conviction must remain in perpetuity. If this conviction fades, then so does your justification for believing it- even if you happen to be rightt!