Some of the things you have to do for the riddles are pretty convoluted, so if you come across a specific riddle, it may be better just to ask about that one.
Solving Pressure Pad Riddles: I only recently figured this out myself after around 30+ hours of play. What you need to do is step on the pads to activate them without touching the ground or anything else. There's nothing you can pick up to place on the pads, and using Explosive Gel or any other tool won't trigger them.
Often, the order doesn't explicitly matter, however, there's usually a manner which is most efficient or that you need to do in order to complete it, even though it's not stated in game (like one where you have to glide back and forth between some buildings, rebounding off the sides).
If you miss a pad, they will all reset and you have to start over. What you need to do to activate them without hitting the ground varies per riddle, but I have found that the Line Launcher and its upgrade, the Line Launcher Tightrope are pretty helpful with these.
Solving the Riddle with the questions marks on the ceiling: What you need to notice for this one is that you can't hit all 3 at once with your Quickfire Batarangs. The third one (the one farthest from you) won't be targeted. You need to hit that one with a Remote Control Batarang either before or after you hit the first two with your Quickfire. Make sure you do this within the time limit!
IGN has a video where they do this. The cut starts after they've already Quickfire triggered the first two Question Marks.
Best Answer
The Inverted Ledge Takedown requires you to stand on a ledge such as a guardrail. Once you have an enemy approaching below you, and you're given the Takedown prompt, wait a few seconds for the enemy to be facing the opposite direction. (i.e.: If you're facing away from the wall, wait until your target is facing the wall) This YouTube video posted in another answer shows exactly how it's done (It should start just a few seconds before the takedown). Basically, the bat is facing the opposite direction of the target when he performs the takedown.
Here's a picture showing the actual takedown (to avoid link rot):
By default:
I played on the Xbox 360, so I'm not 100% on the controls for the PC. If someone makes a correction in the comments, I will edit it into the answer to correct the controls.