I know you said you are an experienced programmer, so I could have put this to you in less words, but I want to be thorough in case somebody with less experience wants to see some kind of working example. The hardware you'll want is a led with a resistor, and optionally a button switch. The led with the resistor goes from digital pin 3 to ground, and the button goes from digital pin 2 to ground. The android app you will want is the Standard Android ADK Demo Kit from the Google play store.
https://play.google.com/store/apps/details?id=com.diyphonegadgets.DemoKit#?t=W251bGwsMSwxLDIxMiwiY29tLmRpeXBob25lZ2FkZ2V0cy5EZW1vS2l0Il0.
The way I got communication going between my ADK board and my galaxy tab was to download this library:
https://github.com/felis/USB_Host_Shield_2.0/archive/master.zip
Change the name of the extracted folder from "USB_Host_Shield_2.0" to "USB_Host_Shield_20" and move it to the arduino libraries folder.
Open the USB_Host_Shield_20 folder and browse to the file "avrpins.h". Open this file in a text editor, like notepad or wordpad, and find the line //#define BOARD_MEGA_ADK and uncomment it by changing it to #define BOARD_MEGA_ADK and then save the file.
There is a sketch in the USB_Host_Shield_20 Examples folder named "demokit_20". Upload it to the Mega ADK board. Now you should be able to press the button and light up "B1" on the adk app, and when you move the slider for "LED 1" on the app, your led should respond by dimming or getting brighter.
I hope this gets you past the hardware hurdle and on to happier programming pastures.