I am using an Ubuntu 14.04 machine as my development machine.
I have worked through the Edison Board Support Package User Guide. I succeeded in building an image and flashing it to my Edison. I succeeded in building the SDK.
What I'm confused about is exactly what is in the SDK and how often it needs to be re-built?
If I add a 3rd party package to the build and re-build the image, do I need to re-build and re-install the SDK?
you mean you Yocto built an image?
If yes: A third party package would end up in build/tmp/deploy/ipk/.... subdirectory. It will be named <package>.ipk.
Just grab the package and opkg install it
Retrieving data ...