The hypersonic research facility where I work is currently involved in this question.
As mentioned above, the orbit of the ISS would eventually decay due to atmospheric drag. Over its life this has been addressed by several methods; at night the solar arrays are rotated to limit the (very tiny amount of) drag from the upper atmosphere, and the space shuttle had on more than one occasion docked with the ISS and used its manoeuvre thrusters to place it back in a higher orbit. Don't quote me on this but I believe this is the main reason for retiring it, now the shuttle is no longer used; there's no way to fix the decaying orbit any more. The fact some of the computers on board are late 90s technology is another reason.
As also mentioned above, letting it fall down naturally is a bad thing; it needs to be deorbited with a degree of precision. It's outside my area but this would likely be done with a small booster mounted on the front of the station. The plan is to aim near the east coast of new Zealand and put it down in the pacific Ocean. This is the main area of interest; if it doesn't break up correctly, some parts might reach the west coast of the USA; parts of mir hit the land instead of the ocean, and mir was a lot smaller then the ISS.
The deorbit profile is also important; it needs to be bought down at a shallow enough angle to allow it to burn up as much as possible (but too slow would risk it being over the USA). Bringing it in at a steeper angle prevents it from reaching the USA but doesn't give enough time for it to burn up, meaning most of it will hit the ocean (or land if someone really miscalculates). Such a large object hitting the ground causes its own problems.
As for what actually happens, this is part of what we've been researching with small scale models in a hypersonic wind tunnel. The solar panels will tear off fairly quickly when it hits the atmosphere. The modules do break apart and tumble away eventually, but there is also some merit in decoupling them from each other first; they spread out more during reentry (more likely of hitting something on the ground) but less likely of coming down in one huge heavy lump.
So as you see, it's a difficult task to do safely.