But it helps to be able to research routings, schedules, and frequencies in advance.
The best websites for checking these (all with English options) are Let's Ferry and our good partner Paleologos SA, where you can find all ferry schedules in Greece and book your ticket online easily and safely.
Assuming you know your starting port – the most likely from Athens are Piraeus, Rafina or Lavrio in that order, or for the Sporades and North Aegean, Volos, and Kavala – it may be easier to use the website for the ferry line which operates from there. The biggest is ANEK (anek.gr/en), Blue Star (bluestarferries.com/en) and Hellenic Seaways (hellenicseaways.gr/en).
Be aware that, unlike buying air tickets online, you cannot actually complete the purchase of ferry, catamaran or hydrofoil tickets from the comfort of your keyboard.
You will pay or at least provide your card details online, and receive a printable confirmation as to seating/berth facilities and car space (if any), but you must proceed to the port in question to retrieve the paper tickets from a representative office.