I recently purchased Moto E with Android 4.4.2 and soon after filled up the internal 4gb with apps.
I installed a 32gb SD card and nothing moves to it. Not even new apps. How can I set the default install location to be the SD card?
You need root access for it, so if you are not rooted, you can manually move the apps to the SD card (if that has been allowed by the app developer) in the Settings->Apps->(App to be moved to SD)->Move to SD Card. Or you can use a specialized linking app, such as App 2 SD, Link2SD or similar (if you have root).