How do I solder a Sparkfun breakout board to a shield?
As far as your question about soldering the gyro sensor to the aeroquad shield goes, if you look a the tiny picture on their website, in the center of the board there is a region marked "gyro".  You'll take the single inline pin strips (also pictured) and break off 7 pins as a group.  Then you'll solder the short end into the gyro board.  Then (unfortunately) it looks like you'll have to solder the gyro board into aeroquad.

As far as shields go, in my experience (Arduino Duemilanove) the spirit behind the shield concept is to allow them to stack up.  The aeroquad "shield" doesn't appear to allow this, so I imagine you'll want to get single inline headers and solder them into the aeroquad so you can plug in the Arduino.

So if you want to add more breakout boards, the general procedure would be to get the headers with the extra long pins, and put those through your protoboards so that other shields can stack on top of them.  This allows everyone access to the pins in the Arduino that they need.