The best site to look at would be at http://www.jadrolinija.hr/ ,because they are main national ferry company in Croatia,it is easy to make your own itinerary because they have list of all sailing schedules,of course including Hvar-Dubrovnik line,so you can chose your desired date and see price and time of departure.
Tickets can be bought in every Jadrolinija office situated almost always in near vicinity of any harbor,or alternatively they can sometimes be bought on the ferry.
Jadrolinija has diverse fleet so you'll be able to travel with car ferry or if you like with a passenger ferry.