Most people take this boat at the end of a slow stretch on Koufonisia, heading back towards the bigger islands. Paros is a good place to land: it has an airport, frequent ships to Piraeus and short hops to Naxos, Mykonos and Antiparos, and plenty of rooms in Parikia and Naoussa if you want a night or two before moving on.
The crossing comes in two speeds. Seajets runs high-speed boats from April to October, and in this direction they are fairly consistent: 1 hr 15 min in most months of last year's data and 1 hr 20 min in April and October. Blue Star Ferries sails all year on conventional ships that call at other islands, so its trip takes between about 2 hr 20 min and 3 hr 35 min.
Frequency matters more than speed on this route. Blue Star sailed only three or four days a week in every month of last year's table, and Seajets ranged from a single weekly run in April to every day in June and October. So pick your sailing first and fit your last nights on Koufonisia around it, especially if you have a flight to catch.
The departure itself is easy. Boats leave from the one harbour on Pano Koufonisi, right beside Chora, so you can usually walk down from your room with your bags. Paros is busier: you arrive in Parikia, the island's main port, where the quay can be hectic in summer.