It's actually pretty easy...
About (non-artillery) siege weapons without the indirect fire promotion:
1) A siege weapon has a range of 2 (3 with the range promotion). You can always shoot into all adjecent hexes.
2) When on a flatland (whether it has a forest/jungle or not doesn't matter), you can shoot the second hex only when the first hex is flatland without a forest/jungle.
3) When on a hill (again, whether it has a forest/jungle doesn't matter), you can shoot into the second hex when the first one isn't a mountain.
4) You can only shoot into hexes without fog of war.
Actually, I'm pretty sure there's another rule: When on a hill, you cannot shoot over a hill that has a forest or jungle on it. So to sum it up:
1. What determines where you can fire is whether you're on flat ground or high ground, and what the tiles directly around you are.
2. You can always fire at the tiles directly around you, so the question is whether you can fire "over" the tiles directly around you (with range upgrade, you need to clear the conditions for firing over both the tile directly next to you, and the tile after that)
3. We have 5 different classes of terrain to take into consideration
-Clear flat ground: Can fire over it no matter where you stand (only kind of tile you can fire over if you're on flat ground)
-Flat ground with forest/jungle on it: Can only fire over it if on high ground
-Clear high ground: Can only fire over it if on high ground
-High ground with forest/jungle on it: Impossible to fire over no matter where you stand, unless you have indirect fire
-Mountains: Impossible to fire over no matter where you stand, unless you have indirect fire
Bonus information: Putting what was previously stated into this formula, tiles with cities on them always count as clear tiles, but they can both be high ground and flat ground, depending whether it was built on a hill. Also, I'm pretty sure these are the exact same rules as with sight radius, so you'll need to take the exact same considerations if you have indirect fire but don't have a unit to spy ahead for you.
I hope I didn't make it unnecessary complicated, I just like summing things up comprehensibly. Need to hold myself back before I start putting this information into a chart.