I just got the Arduino Mega Protoshield, and I am not entirely sure how I can solder this. Does it matter which side I solder on? Can I have wires soldered on both sides (not soldered to the same hole)? I've been using breadboards and haven't used a prototyping board before (I do have some experience soldering, though). Any advice would be appreciated! I am planning on stacking two protoshields on an Arduino Due.
You can do anything you wish that works. Just be careful when you solder.
Top, bottom, over the end- whatever you need to make it work as long as you don't have interference problems with the Mega. Pay attention to the usb connector, so you don't short on it.
It's always best to keep things neat and tidy, making it easier to spot problems and to help see what is what. Multiple colors for wires, which are trimmed to length and in some sort of order help as well.