You can get to some of the islands such as Mykonos and Santorini by air, but most of the other islands are reached by ferry from Athens. The ferries are regular and there are ticket operators at the harbors, so you can also use them to visit other islands during your stay. You can also rent a car or a bike, or use the local bus system to navigate your own way around the islands.
Any option you chose, you can’t go wrong with the Greek Islands as your next destination. Your trip will surely be a blast!