I spent 10 days there this summer and it�s amazing!
We caught the ferry from Ancona in Italy (Ryan Air fly direct there) using the local ferry company -
http://www.jadrolinija.hr/default.aspx?lang=2 The ferry drops you in Split where you can change to another ferry which takes you to Hvar Island. Once there you can catch a bus which waits for the ferries to drop off passengers. The bus takes you into town and at the bus station you bargain with locals who rent their rooms out to tourists. This is one of the main sources of income for them so they prefer it if you stay at least 3-4 nights. We got a double room for 25 euros per night each, fairly reasonable but you can get them cheaper; just depends on the time of year and your bargaining skills!
Hvar is great, it has a great vibe to it and there are many activities available; scuba diving, fishing, or just hanging on the beach.
http://www.hvar.hr/
The other main islands are Korcula, Brac and Mijet although there are about 1000 islands that dot the Croatian coast.
I would recommend starting in Hvar and making your way down through the islands to Dubrovnik; one of the most beautiful places I�ve been. It�s a walled city and a Unesco world heritage site and simply has to be seen to be believed. A definite must do in Croatia.
I could go on forever but I won�t; go and have a great time and see for your self.