Here's a lovely photo album of a Day Out in Aegina ... pictures of the whole experience ... including the ferry over & back, and going onto the Metro Platform back to Central Athens, & validating one's ticket. http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/    
Two small added tips: (1) there are hydrofoils and conventional ferries.  Do NOT choose the former... they are closed in , with no view. Ferries take just a bit longer with lovely open decks to sit on, and enjoy the seascape the bay, and all the other vessels. 
(2) you're a newcomer to Greece; the Green Line ferry to Piraeus is fastest way, plus only €1.30 fare I think.  But u should know... altho Greece has almost NO pickpocketing compared with Italy or Paris, the Green Line is favored by a small ring of pickpocketers (because of so many clueless cruise passengers).  Keep your papers/cash in a zippered handbag w.  your hand on the zip, if a woman, or in a moneybelt if a man (men seem to be the chief victims of thieves because they insist on keeping their wallets in their pockets). Just be prudent; I've used this Metro countless times in my 12 trips to greece, and never an incident.  BTW,  while walking around in Athens, elsewhere, no need to carry one's passport, driver license & all money; just take what you'll need for the day, leave the rest locked in a suitcase or in hotel safe.