Connecting MPU6050 to Arduino Lilypad
Since you seem to need some orientation, I will explain a few things, to get you started.

The MPU6050 is a device, that communicates through the I2C interface. It uses 2 communication lines (SCL for the clock and SDA for the data). To use is with the Lilypad, you have to connect those two lines, Vcc (5V) and Ground. If you look at a pinout diagram, you can identify, which of the pads are SDA and SCL on the Lilypad.

It is up to you, if you connect the mentioned lines via soldering or by other means. Normally you would solder connecting wires between the MPU6050 and the Lilypad. If you want the MPU to be removable, you can solder a cable with a pin header (for example female) to the Lilypad and the according pins to the MPU (for example a male pin header). That way, you could also stick the MPU to the board and remove it again if necessary. How you are doing it is not important, as long as the electrical contact is good.



There are also a lot of tutorials and ready to use libraries for the MPU6050 on the net. newbie already posted a link to a tutorial. Also Adafruit has a library on github with examples, that explain how to use it. That way you should be able to get started with your project.

Good luck!