Ok, what is the MPU-6050?
In short, it’s a gyroscope, accelerometer and temperature sensor all in one package. It’s a 3.3V device and uses I2C to communicate. (The device also has a second I2C bus for slave devices.) The device can do some filtering, store selected measurements into a FIFO buffer, detect simple stuff like free fall, motion and zero motion and it has a built in “DMP” not covered by the device’s documentation.
Where can you get one?
SparkFun sells breakout boards: https://www.sparkfun.com/products/11028 Check out the reseller page, if you don’t live in the USA, to find a more local vendor. Also DX (in China) sells very inexpensive breakout boards. Just type “6050” into the search bar.
The Arduino playground has a good short descritpion of the MPU-6050, a list of different breakout boards and example code you can copy and paste directly into the Arduino IDE.
How to undestand the operation of the MPU-6050?
I don’t think there is any other way than reading the manuals in order to understand what can be done with this device. You’ll need to read the Product Specification (PS) and the Register Map and Descriptions (RM) documents for the MPU-6050. Both can be found at Invensense’s website. In my opinion, the PS seems to be written by the marketing department. It gives you a general overview. The RM is the real deal, except it currently does not cover the much advertised DMP-functionality. However, it will explain the basic functionality of the registers.