The most convenient way to travel from Heraklion to Rethymno is by taxi, which costs approximately 70 EUR.
If you prefer a more budget-friendly option, you can take the bus, but it involves several connections. From the airport, catch bus #1 or 78K to bus station A, located in the eastern part of Heraklion (the bus stop is 50 meters from the terminal exit, with a fare of 1.2 EUR and a travel time of 15-20 minutes). From there, purchase a ticket for a regional bus that will take you to Rethymno. The schedule for the Heraklion-Rethymno bus can be found here, with a ticket price of 8.30 EUR.
You can find more information about buses in Crete here.