Public transport is well developed in Croatia, especially in the tourist areas. As long as you want to reach a popular resort, you will generally have no problem getting there.
Major tourist cities are served by airports. There are airports in Rijeka, Pula, Split, Zadar, Dubrovnik, Mali Losinj and Brač island. These cities are connected by flights to the capital Zagreb. There are a lot of direct flights from European countries to the seaside destinations during the summer. Domestic flights are not very popular, as most locals use their cars to reach various cities. There is no problem however to take a plane to Zagreb and then continue with a different flight to your final destination.
The rail network may not be as extensive as in Germany or the UK, but it is in a very good shape and also improving. As you may expect, popular summer destinations are very well served by trains. Zagreb is connected directly to Rijeka and Split. If you want to go to a smaller resort, you will likely need to take a bus or a taxi from a train station nearby to the final destination. There are some new high-speed trains that are currently introduced, so you may be lucky and travel in very good conditions on some routes.
It is important to mention that it is not currently possible to reach Dubrovnik by train, even if this is one of the most appreciated destinations. This is likely because the train would have to cross Bosnia and Herzegovina for a short distance. You can travel by train however to Split and then take a bus or a ferry. You can find more information on the trains in Croatia from the Croatian Railways website.
Since the railway network is not yet as extended as it should be, the bus network is very well developed. You can get almost anywhere by bus, the travel conditions are very good and the prices are not high. The buses are useful not only to travel within the country, but also to reach Croatia from neighbouring countries. There are a lot of international routes from Italy, Hungary, Serbia, Bosnia and Herzegovina. There is no central company or certain authority maintaining timetables and fares for all the bus companies, so you have to do some research before in order to find information on the route that you need. Here are a few websites however, so you have a good starting point with your research: Autobusni Kolodvor Zagreb (Bus Terminal Zagreb), AP Varazdin, Autotrans, Croatia Bus, Libertas Dubrovnik.
The most tourist destinations are located along the coast, so there are very good and convenient ferry services connecting them. Croatia is also very well connected to Italy. Most ferries take both passengers and cars. While the fares for passengers are quite cheap, those for taking your car on the boat are higher.
Many tourist resorts are located on islands, so you definitely need to take a ferry to reach your destination from the mainland. Ferry schedule is adapted to the needs of the tourists during summer, so it is easy to find something according to your requirements. The main ferry company is Jadrolinija, which operates a lot of local and international routes.