A few days ago, Arduino just released a "start pack" for Android developers: http://arduino.cc/en/Main/ArduinoBoardADK
The Arduino ADK is a microcontroller board based on the ATmega2560 (datasheet). It has a USB host interface to connect with Android based phones, based on the MAX3421e
I have been searching again and again for tutorials or something in order to begin Arduino programming, and I am looking for very good tutorials, maybe some kind of "hello light" that would make a light blink on the card with a button on my Android device.
Have you got some links, fan blogs, other information about that topic?
I, of course, know the Arduino website and Android developer documentation, but they are quite over-complicated...
You are asking a two part question: (1) How do I program Arduino? (2) How do I use the Android ADK to do stuff with Arduino.
For part one you're going to need to get hardware since the Arduino site is pretty straightforward about how to get started.
For part two you're going to have to have a ADK compatible Android device which as of July 2011 is either a Nexus One, Nexus S, or Motorola Xoom.
If you have one of these devices, you'll need an Arduino which can run the ADK (see your question). And of course the best documentation is still
Just realize that you'll be writing two programs, one that runs on the Arduino in C/C++, the other on Android in Java.
Update:
Since you were asking for blogs or how-tos, MAKE does have some tutorial which may be what you are looking for at Makezine.