First off, it's not guaranteed that there was a Jesus at all. It's pretty likely, all up, but there's no available physical evidence. Religious historians work from a set of documents about his life, most of which likely reference one another anyway. The most famous of these documents are of course the four Gospels that were selected for the Bible. There were many other Gospels which weren't.
Here is an apologetic site which argues that Jesus claimed to be God, or the son of God, or whatever. (I won't get into the whole Trinity argument about whether the two are separate.) The support given is exclusively Gospel quotes, and all but two of them are from John. Even the John quotes are not all explicit or delivered in the first person, especially when you consider the idea that we're all God's children, and He's everyone's Father.
Jesus himself probably never wrote a word in his life. It's not surprising given that literacy in the area was about 3%. Everything he said, if he said it, is filtered through at least one chronicler, or journalist if you like. That's even before translation and interpretation began. Nothing about him is straight from the horse's mouth.
Furthermore, none of the four Gospels was written within 20 years of Jesus' death. As far as we know, nothing was written about him in that time. The fact that the life expectancy was 25-30 years casts doubt on two things: that his actual companions wrote the Gospels named for them, and that the people who saw him would still be alive and able to corroborate or contradict the accounts (again, remember the literacy rate). Perhaps there was a reason the writers waited.
There's a major line of apologetic which argues that Jesus would not have sacrificed himself if he had not believed in his own divinity, and the apostles would not have carried on his message if they hadn't witnessed the resurrection with their own eyes. I've discussed that elsewhere. I won't deny that it can be a compelling argument, because it convinces a lot of people. That's not to say that it's necessarily sound.
Even if you accept a priori that Jesus and the apostles were all sincere, which I personally doubt, there are still ways in which they could be mistaken. One way is if a false resurrection was perpetrated by other people entirely, using a Jesus double. The Bible suggests that very few people actually saw Jesus after his death anyway, and were convinced simply by the empty tomb. If that's all it took to convince the average Israelite, hoaxers must have had it pretty easy back then.
With my kind of brain, I look at it probabilistically. One estimates for oneself the probability, given the assumption that the accounts of Jesus are mostly accurate, that he was actually divine and not just lying for a good cause or honestly mistaken. One then estimates the separate probability that the accounts of Jesus really are mostly accurate.
One then has to multiply the two probabilities together (converting into fractions first), and if they come to 50% or more then it's more likely than not (though not at all certain) that Jesus was divine. For that to happen, the two probabilities need an average of at least 70.7%. I'm not that sure by a long shot. How about you?