First of all, verify that you have checked the box in android settings to allow installation of unverified packages, but once that has been done, its as simple as putting the APK on a jump drive / SD card, or even SSH if you are familiar with the Android command line. The built in file manager is simple to use, just navigate to the drive, and install the apk
Just sent this to another user. You'll need the Android SDK on you machine (PC). Connect PC USB to microUSB OTG port on UDOO. Run adb (in Android SDK folders) from command line to install APKs. There is a good deal of information about adb (Android Debug Mode) in the Google SDK support site. http://developer.android.com/tools/help/adb.html Also note that, like with any Android device, your UDOO needs to be in debug mode (under developer settings) for this to work. There is no GApps support or community introduced option for GApps at this time. But I suspect there will be.
In add of this, for have adb connecting to the board, you need to set the "External OTG port enabled" flag in the same section of debug just pointed. This because the UDOO board share the OTG line beween Arduino and external port used for adb upload and debug.
to help me understand, could you explain more what you want to do? 1. you have created an Android app and you have now an .apk ready to be installed. 2. you want to use UDOO as an Android device for testing you application while you're still developing it in Eclipse.