Connect the TX of the atmega32 to on of the RX pins on the arduino mega2560 (don't use serial0 - as that's what's connected to USB serial and it will fight with the USB serial adapter), and vice versa, and connect the grounds (as always).
Make sure the program on both boards is communicating on the serial port you're using and at the same baud rate, and you should be good to go - data sent by one will be received by the serial port of the other. If they're both running an Arduino sketch, you'd be sending data with Serial1.print() (or whatever serial port you're using), and checking for received characters with Serial1.available() and reading them out with Serial1.read().