I recently found out about a wide variety of tutorials and guides that help you make cheap arduino compatible circuits for embedding in projects permanently without wasting arduino boards in the process. If I were to make my own arduino compatible circuit, or purchase one such as adafruit's Boarduino, would I still be able to use shields, such as the Phi-2 shield? I understand the form factor is different, so you can't simply plug it into the board as with a standard arduino, but if I look at all the pins the shield is supposed to connect to and route them to the correct pins on the Boarduino with wires, the shield should work fine, right? I'm really new to this type of stuff, so I want to make sure I understand this correctly. Thank you!
Yes, as long as you route the right signals and power to the right pins it will work fine.
The Arduino’s headers just connect direct to the AVR chip’s pins.
Yes, one can do all kinds of neat things with some perfboard - even wire in a new processor to use the arduino card as part of a test bed. Here's an Uno board being used for USB & power to prototype a bigger processor