After 1967, a few Jewish settlers moved into eastern Hebron, where they live under continual Israeli army protection. The rest of the city is Palestinian, and the city is now divided in two (with lots of soldiers patrolling the dividing line). The Cave of Machpelah, Abraham's burial place and the main holy site in the city, is on the border between the Arab and Jewish sectors.
There are probably Palestinian buses from Bethlehem to the Arab side of Hebron.
The Cave of Machpelah is the main religious site in the city. The cave itself is deep underground, and now people pray in a building on top of it, which was built by King Herod about 2000 years ago.
Most of the time, half of the building is used for Muslim and half for Jewish prayer. On a few predetermined days each year, each religion gets to use the entire building. For the Jews, in addition to the normal holidays, one of these days is "Shabbat Chayei Sarah" each fall, on which thousands of people from all of Israel visit Hebron to commemorate Abraham's purchase of the Cave from its previous Hittite owners.