The Pi has two UARTs which can be used for serial communications. See https://www.raspberrypi.org/documentati ... on/uart.md
. The Arduino can also do serial communications through USB and also via the RX and TX pins. However, the Pi uses 3.3V logic and the Arduino varies by board type. The Nano uses 5V I think. You will need a logic level converter between them. Your connections will be Pi RX to Ard TX via converter, Pi TX to Ard RX via converter and Pi Gnd to Ard Gnd directly. You will also need to set the communication parameters (baud rate, stop bits, parity, etc) the same at each end.
There are a number of Arduino libraries to use an MPU6050. The Jeff Rowberg library was the main one for a long time, but there are others (FreeIMU, Electronic Cats, etc). These are often based on Jeff's original code.