What did he really do? Did he really claim that he is the son of God? What are the differences between the historical facts and the teachings in the Bible about him?
The short answer is not much. What we know comes from critical analysis of the synoptic gospels, anthropological and archeological facts about the region that we can use to interpret those texts, and Roman writings from the time period, most importantly those of Jewish-Roman historian Josephus. There's a whole field of scholarship on the historical Jesus, and you should check out the work of the Jesus Seminar(http://en.wikipedia.org/wiki/Jesus_Seminar). I can recommend a couple books on the subject as well: If you want the full monty, big ol' weighty tome, you need John Dominic Crossan's The Historical Jesus: The life of a Mediterranean Jewish Peasant. -http://www.amazon.com/The-Historical-Jesus-Mediterranean-Peasant/dp/0060616296
For the shorter, more digestible version, see his book Jesus: A revolutionary Biography http://www.amazon.com/gp/product/006180035X/ref=pd_lpo_sbs_dp_ss_1?pf_rd_p=1535523722&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0060616296&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=1QHBK1Y6G36CNGSTPAZ7
For a counterpoint to many of Crossan's arguments, see Dale Allison, Jesus of Nazareth http://www.amazon.com/Jesus-Nazareth-Millenarian-Dale-Allison/dp/0800631447
New Testament Scholarship is a really interesting field and if you really want to answer the question you've asked here you should check out the work these historians/religious studies scholars have been doing in the last 20-30 years.