first, it is very important to have a level converter (e.g. DeLock Converter USB 2.0 male > Serial TTL) because the µCs serial Port on the Raduino-Board will be toasted if you connect it directly to the computers serial port.
Connect the four wires from the Nextion to the Converter and make sure, that RX and TX Lines are crossed (RX-Line from Nextion to the Converters TX Line and TX-Line from the Nextion to the converters RX-Line).
Load the .hmi-File which belongs to your display into the Nextion-Editor and press the upload-button.
The Nextion-Editor tries to find the converters serial port automatically, otherwise you have to choose it manually in the dropdownbox.
Press the GO-Button and the file should now be transfered to the Display (this will take a little while and you can see the upload status on the display).
When the upload is finnished, disconnect the converter and connect the display to the raduino board.