Usually breaks are caused by humans (ships pulling anchors, sabotage/spying). Sometimes they're natural (caused by wildlife, ocean floor movement, flaws in the cable design).
Fixes usually take a few hours if they happen at the endpoints, or weeks if they happen somewhere under the ocean.
Interestingly, spying breaks always involve three simultaneous breaks in the cable. The cable is broken at two points, and then broken at a third point in the middle to put spy equipment. They do this so the people operating the cable can't tell where the spy equipment was inserted, since otherwise you can tell where a cable is broken or being tampered with by sending light down the cable and seeing how long before light reflects off the broken bit and comes back to the end.
Using statistical methods, you can see how frequently you'd expect a cable to break at different points along it's length simultaneously, and it happens a lot more than raw chance would suggest.